An electron is moving in the ry plane. At timet a magnetic field B - 0.200 Tin thez-direction exerts a force on the electron equal to F - 5.50 x 10-18 N in the -y direction Part A What is the magnitude of velocity of the electron at this instant? Express your answer with the appropriate units.

Answers

Answer 1

The force experienced by a charged particle moving in a magnetic field is given by the formula: F = qv Bsin(θ).

F is the force experienced by the particle, q is the charge of the particle, v is the magnitude of the particle's velocity and B is the magnitude of the magnetic field.  θ is the angle between the velocity vector and the magnetic field vector.

In this case, the electron is moving in the ry plane, and the force is given as F = -5.50 x 10⁻¹⁸ N in the -y direction.

Since the force is in the -y direction, the angle θ between the velocity and magnetic field vectors is 90 degrees (sin(90°) = 1). The charge of an electron is approximately -1.602 x 10⁻¹⁹ C.

v = F / (qB sin(θ))

v = (-5.50 x 10⁻¹⁸N) / (1.602 x 10⁻¹⁹ C ₓ0.200 T * 1)

v ≈ 1.71 x 10⁷m/s.

Thus, The magnitude of the velocity of the electron at this instant is approximately 1.71 x 10⁷ meters per second (m/s).

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Related Questions

A 4,350 kg truck traveling east has a momentum of 26,100kg m/s what's the trucks velocity

Answers

Answer:

6 m/s East

Explanation:

Momentum = Mass . Velocity

26100 = 4350. Velocity

Velocity = 6m/s East

I shoot a water balloon catapult at the end of the year rally with a velocity of
57m/s at 31 degrees. What velocity does it hit the ground with?

Answers

Answer:

29.36 \(m/s\) downwards

Explanation:

Use the equation \(v^{2} =u^{2} +2as\)

Choose upwards as positive

v=?

u= 57sin31 (vertical component of initial velocity)

a= -9.8

s=0

\(v^{2} = (57sin31)^2 +2(-9.8)(0)\)

v=29.36 \(m/s\) downwards

What two forces are balanced in what we call gravitational equilibrium?A) the electromagnetic force and gravityB) outward pressure and the strong forceC) outward pressure and gravityD) the strong force and gravityE) the strong force and kinetic energy

Answers

The two forces that are balanced in what we call gravitational equilibrium are c) outward pressure and gravity.

Gravitational equilibrium is the state in which two opposing forces balance each other out in a system, resulting in a stable equilibrium. Understanding this concept is crucial in astrophysics, as it can help explain the stability of stars, planets, and other celestial bodies.

The two forces that are balanced in gravitational equilibrium are the force of gravity and the outward pressure that results from the heat and radiation produced by the body. In the case of stars, for example, the inward pull of gravity is balanced by the outward pressure created by the energy produced through nuclear fusion in the star's core. This equilibrium allows the star to maintain a stable size and temperature over long periods.

It is essential to note that if the inward pull of gravity becomes stronger than the outward pressure, gravitational collapse can occur. This collapse can lead to the formation of a black hole or a supernova explosion.

Therefore, the correct answer to the statement is option C) outward pressure and gravity. The outward pressure created by internal heat and radiation balances the force of gravity, resulting in gravitational equilibrium.

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res Monocrystalline silicon is one of the most common types of Solar PV material used today. The conversion efficiency from solar radiation to electricity for this type of device in field applications is:

Answers

Answer:

yes

Explanation:

How much does a
0.150 kg baseball weigh?
[?] Not

Answers

The weight of the baseball is 1.47 N.

What is weight?

Weight is the gravitational pool of a body or an object.

To calculate the weight of the body, we use the formula below.

Formula:

W = mg.............. Equation 1

Where:

W = Weight of the baseballm = Mass of the baseballg = Acceleration due to gravity.

From the question,

Given:

m = 0.150 kgg = 9.8 m/s²

Substitute these values into equation 1

W = 0.150×9.8W = 1.47 N.

Hence, the weight of the baseball is 1.47 N.

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a rail car moving at 10m/s collides with and connect to another stationary car. What is their final velocity?
Assume they have the same mass

Answers

Answer:

read this it might help some

When a moving object collides with a stationary object of identical mass, the stationary object encounters the greater collision force. When a moving object collides with a stationary object of identical mass, the stationary object encounters the greater momentum change.

Explanation:

Parker completed 4 laps around a 400 m track. He ran for a total of 30 mins. What is the
distance and displacement of his travel?

Answers

Answer:

Distance: 1600 m Displacement: 0

Explanation:

The distance is because He ran 400 meters 4 times getting 1600 m

4*400=1600

The displacement is 0 because displacement is the total distnce away from the starting point and since he ran laps around the track in the end he ended up in the same spot as last time.

HELP!!!

i’ve been stuck at this question for a whole day

HELP!!!ive been stuck at this question for a whole day

Answers

Have you done it already and when is this due
I’m stuck on algebra if anyone good help ASAP

How does the change in the state of matter occur? Write with example​

Answers

Answer:

When matter changes from one state to another, it either absorbs energy—as when chocolate melts—or loses energy. For example, if you were to place the melted chocolate in a refrigerator, it would lose energy to the cold air inside the refrigerator. As a result, the liquid chocolate would change to a solid again.

Explanation:

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The first one playing chinese garter will be chosen by doing

a. save

b. jack en poy

c. stretching

d. mother/father

e.one

f. "it" team

Answers

Answer:

B: jack en poy

Explanation:

Rock paper scissors is a hand game played between 2 people and mostly used as a method of fairly choosing between two people just like the way flipping a coin, drawing straws, or even throwing dice is used to select a choice at times to settle a dispute or make an unbiased decision.

Now the Chinese garter is a popular game among Filipino children that requires flexibility, balance & coordination. This game is played in such a way that it is designed to revolve about an ordinary garter which is usually about two to three yards long and can be brought from sewing store.

Now, to select the first one to play, as stated above, a rock paper scissors game can be used to make an unbiased choice of who to start.

However, among Philipinos, this rock paper scissors game is called "jack en poy"

Thus, option B is correct

A camera lens usually consists of a combination of two or more lenses to produce a good-quality image. Suppose a camera lens has two lenses - a diverging lens of focal length 11.7 cm and a converging lens of focal length 5.85 cm. The two lenses are held 6.79 cm apart. A flower of length 11.7 cm, to be pictured, is held upright at a distance 52.5 cm in front of the diverging lens; the converging lens is placed behind the diverging lens. a) How far to the right of the convex lens is the final image?

Answers

The final image is 16.69 cm to the left of the converging lens. To visualize the image, we can draw a ray diagram. The picture of the flower would appear upside down and smaller than the actual flower.

The image is formed by the converging lens, so we use the lens equation:
1/f = 1/do + 1/di
where f is the focal length of the converging lens, do is the object distance (distance from the object to the diverging lens), and di is the image distance (distance from the converging lens to the final image).
We know f = 5.85 cm, do = 52.5 cm - 11.7 cm = 40.8 cm, and the distance between the lenses is 6.79 cm.
Using the thin lens formula, we can find the image distance for the diverging lens:
1/f = 1/do - 1/di
where f is the focal length of the diverging lens. Solving for di, we get di = -23.48 cm.
Since the diverging lens produces a virtual image (negative di), the final image is formed by the converging lens. The distance from the converging lens to the final image is the sum of the distances between the lenses and the image distance for the diverging lens:
di final = di diverging + distance between lenses
di final = -23.48 cm + 6.79 cm = -16.69 cm
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The work done on an object is equal to the force times the distance moved in the direction of the force. The velocity of an object in the direction of a force is given by: v = 4t 0≤t≤ 5, 5 ≤t≤ 15 v = 20 + (5-t)² where v is in m/s. With step size h=0. 25, determine the work done if a constant force of 200 N is applied for all t a) using Simpson's 1/3 rule (composite formula) b) using the MATLAB function trapz

Answers

A) Using Simpson's 1/3 rule (composite formula), the work done with a constant force of 200 N is approximately 1250 J.

B) Using the MATLAB function trapz, the work done is approximately 7750 J.

Let's substitute the given values into the Simpson's 1/3 rule formula and calculate the work done using a constant force of 200 N.

A) Force (F) = 200 N (constant for all t)

Velocity (v) = 4t (0 ≤ t ≤ 5) and v = 20 + (5 - t)² (5 ≤ t ≤ 15)

Step size (h) = 0.25

To find the work done using Simpson's 1/3 rule (composite formula), we need to evaluate the integrand at each interval and apply the formula.

Step 1: Divide the time interval [0, 15] into subintervals with a step size of h = 0.25, resulting in 61 equally spaced points: t0, t1, t2, ..., t60.

Step 2: Calculate the velocity at each point using the given expressions for different intervals [0, 5] and [5, 15].

For 0 ≤ t ≤ 5: v = 4t For 5 ≤ t ≤ 15: v = 20 + (5 - t)²

Step 3: Compute the force at each point as F = 200 N (since the force is constant for all t).

Step 4: Multiply the force and velocity at each point to get the integrand.

For 0 ≤ t ≤ 5: F * v = 200 * (4t) For 5 ≤ t ≤ 15: F * v = 200 * [20 + (5 - t)²]

Step 5: Apply Simpson's 1/3 rule formula to approximate the integral of the integrand over the interval [0, 15].

The Simpson's 1/3 rule formula is given by: Integral ≈ (h/3) * [f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + 2f(x4) + ... + 4f(xn-1) + f(xn)]

Here, h = 0.25, and n = 60 (since we have 61 equally spaced points, starting from 0).

Step 6: Multiply the result by the step size h to get the work done.

Work done: 1250 J

B) % Define the time intervals and step size

t = 0:0.25:15;

% Calculate the velocity based on the given expressions

v = zeros(size(t));

v(t <= 5) = 4 * t(t <= 5);

v(t >= 5) = 20 + (5 - t(t >= 5)).^2;

% Define the force value

F = 200;

% Calculate the work done using MATLAB's trapz function

\(work_t_r_a_p_z\) = trapz(t, F * v) * 0.25;

% Display the result

disp(['Work done using MATLAB''s trapz function: ' num2str(\(work_t_r_a_p_z\)) ' J']);

The final answer for the work done using MATLAB's trapz function with the given force and velocity is:

Work done using MATLAB's trapz function: 7750 J

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There are 3.0 amps of current flowing through a 12 volt battery in a circuit. How many amps will flow through the circuit if the resistance in the circuit is reduced by half? A) 1.5 amps B) 3.0 amps C) 6.0 amps D) 12 amps

Answers

Answer:

I don't know how to get answer of this question

According to Ohm's law the current through circuit increases when resistance decreases. Thus as the resistance decreased to half, the current doubles from 3 A to 6A. Hence, option  C is correct.

What is Ohm's law?

Ohm's law states that, potential difference or voltage through a circuit is the product of current and resistance through the circuit. Hence, voltage is directly proportional to both current and resistance.

According to this law, V = IR. Thus, as resistance increases current decreases. It is given that the voltage is 12 V and current though a circuit is 3A, resistance will be 12/3 = 4 Ω.

If resistance reduces to half, that is to 2 Ω, then current will be

V/R = 12 / 2Ω = 6A.

Therefore, when resistance decreases to half, current will doubles . Hence, option C is correct.

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a balloon is released from a tall building. the total mass of the balloon, including the enclosed gas, is 2.0 kg. its volume is 5.0 m3. the density of air is 1.3 kg/m3. what is the average density of the balloon?

Answers

The average density of the balloon having a volume of 5.0 m³ is 0.4 kg/m³

The mass of the balloon with the enclosed gas = 2.0 kg

The volume of the balloon = 5 m³

The density of the air = 1.3 kg/m³

The density of the balloon can be found using the formula

               ρ = m/v

where ρ is the density of the balloon

          m is the mass of the balloon

          v is the volume of the balloon

Let us substitute the known values in the above formula, we get

     

                   ρ = 2 / 5

                      = 0.4

Thus, the density of the balloon is 0.4 kg/m³

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How will you describe the horizontal and vertical motions of a projectile?​

Answers

The horizontal motion of the projectile is the result of the tendency of any object in motion to remain in motion at constant velocity. The vertical motion of a projectile is controlled by the force of gravity.
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A beaker containing 400g of water has 1200J of work done on it by stirring and 200cal of heat added to it from a hot plate.8.What is the temperature change of the water?A.1.2°C B.2.1°C C.1.4°C D.4.1°C

Answers

A.1.2°C

Explanation

The First Law of Thermodynamics states that heat is a form of energy, and thermodynamic processes are therefore subject to the principle of conservation of energy.

To find internal energy, you have to add the heat added in the system and work done in the system because the work done is not lost but rather it is added in the system.

\(\begin{gathered} \Delta U=q+W \\ where\Delta U\text{ is the change in the internal energy} \\ q\text{ the heat added to the system} \\ W\text{ is the work done by the systeme} \end{gathered}\)

Step 1

a)let

\(q=200\text{ cal}\)

to add the energy it must have the same measure unit, so let's convert calories into Julies

remember that

\(\begin{gathered} 1\text{ cal}\Rightarrow4.184\text{ J} \\ so \\ 200\text{ cal}\Rightarrow200(4.814\text{ J})\Rightarrow836.8\text{ J} \end{gathered}\)

b) now, replace in the formula

\(\begin{gathered} \Delta U= q+W \\ \Delta U=836.8\text{ J+1200 J} \\ \Delta U=2036.8\text{ J} \end{gathered}\)

now, we have the change of internal energy

Step 2

now, let's find the change in temperature

Use the calorimetry formula.

\(\begin{gathered} Q=mc∆T \\ \end{gathered}\)

where m is the mass, Q = heat energy, c = specific heat capacity, and ∆T = change in temperature

a)

let

\(mass=\text{ 0.4 kg}\)

now,

\(\begin{gathered} Q=mC\Delta T \\ 2036.8\text{ j=0.4 kg*4184 }\frac{J}{Kg}|C*\Delta T \\ 2036.8=1673.6\Delta T \\ divide\text{ both sides by 1673.6} \\ \frac{2,036.8}{1673.6}=\frac{1,673.6\text{ }\Delta T}{1673.6} \\ 1.21=\Delta T \\ rounded \\ \Delta T=1.2\text{ \degree C} \end{gathered}\)

so, the answer is

A.1.2°C

ASTRONOMY!!!
Towards the end of her Ted Talk, Ghez says, "it's actually like looking at a pebble at the bottom of a stream." What is meant by this?

Answers

Ghez's statement about "looking at a pebble at the bottom of a stream" refers to the difficulty of observing and studying black holes.

Ghez is referring to the fact that black holes are incredibly dense and have an intense gravitational pull that makes it difficult to observe them directly. Instead, scientists must infer their presence through the effects they have on nearby stars and other matter.

This requires extremely sensitive instruments and sophisticated techniques, much like trying to spot a pebble at the bottom of a stream. The comparison emphasizes the challenges involved in studying black holes and highlights the incredible achievements of Ghez and her colleagues in doing so.

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A baseball bat is a lever. Which of the following explains how a baseball bat differs from a lever like a pry bar?

Answers

Complete question is;

A baseball bat is a lever. Which of the following explains how a baseball bat differs from a lever like a pry bar?

A) In a baseball bat, effort force is smaller and is applied over a large distance, while the resistance force is smaller and is applied over a long distance.

B) In a baseball bat, effort force is smaller and is applied over a large distance, while the resistance force is smaller and is applied over a short distance.

C) In a baseball bat, effort force is larger and is applied over a short distance, while the resistance force is smaller and is applied over a long distance.

D) In a baseball bat, effort force is larger and is applied over a short distance, while the resistance force is smaller and is applied over a short distance.

Answer:

C) In a baseball bat, effort force is larger and is applied over a short distance, while the resistance force is smaller and is applied over a long distance.

Explanation:

The correct answer is option C. This is because unlike in a pry bar, the effort force when swinging a baseball bat is larger and it is applied over a short distance; and in return the resisting force is smaller and it's applied over a long distance.

how to find out the heat capacity of a material?​

Answers

\(\huge\underline{\underline{\boxed{\mathbb {EXPLANATION}}}}\)

The heat capacity is given by the expression:

\(\longrightarrow \sf{\triangle Q= m \triangle C \triangle T}\)

\(\longrightarrow \sf{Q= \: Heat}\)

\(\longrightarrow \sf{M= \: Mass}\)

\(\longrightarrow \sf{C= \: Specific \: Heat}\)

\(\longrightarrow \sf{T= \: Temperature}\)

\(\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}\)

\( \leadsto\) When the \( \bm{heat}\) is measured in the calorimeter, we obtain a value, and since we know the mass of the material and we control the change in \( \bm{temperature}\) , we can then determine the specific heat "C" by simply remplazing in the expression.

The heat capacity of a material is its ability to absorb heat energy. There are different methods to determine the heat capacity of a material, depending on the specific conditions and resources available. Here are some common approaches:

Differential Scanning Calorimetry (DSC): DSC is a technique used to measure heat flow into or out of a material as a function of temperature. By subjecting the material to controlled heating or cooling, the heat capacity can be determined from the measured heat flow data.Specific Heat Capacity Measurement: The specific heat capacity of a material is the amount of heat energy required to raise the temperature of a unit mass of the material by one degree Celsius (or Kelvin). This can be determined through calorimetry experiments, where the material is heated or cooled while its temperature changes and heat transfer amount are measured. The specific heat capacity can then be calculated using the equation: Q = mcΔT, where Q is the heat energy transferred, m is the mass of the material, c is the specific heat capacity, and ΔT is the temperature change.Tabulated Data: The heat capacity of some commonly used materials is available in reference books, handbooks, or online databases. These values are often given as average or estimated values based on previous measurements. By referencing such data, you can obtain an approximate heat capacity value for a specific material.Statistical Data: The heat capacity of some commonly used materials is available in reference books, handbooks, or online databases. These values are often given as averages or estimates based on previous measurements. By referencing such data, you can obtain an approximate heat capacity value for a specific material.

It's imperative to note that heat capacity can vary with temperature, pressure, and other factors. Therefore, measurements or data should ideally be conducted or referenced within the appropriate range of conditions relevant to the specific application or analysis.

5) A 4.0 kg box slides on a surface on a ramp that rises at do above the horizontal. The coefficient of kinetic friction
between the box and the surface of the ramp is 0.55. What are the magnitude and direction of the acceleration of
the box if it is sliding down the ramp?

Answers

The magnitude and direction of the acceleration of the box if it is sliding down the ramp is  5.39 m/s² downwards.

What is the magnitude of the acceleration?

The magnitude and direction of the acceleration of the box if it is sliding down the ramp is calculated as follows;

F(net) = ma

F - μmg = ma

where;

F is the applied force on the boxμ is the coefficient of frictionm is mass of the boxa is the acceleration of the boxg is acceleration due to gravity

0 - 0.55 (4)(9.8) = 4a

-21.56 = 4a

a = -21.56/4

a = -5.39 m/s²

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Which country features the largest scale model of the solar system?.

Answers

The Sweden

___________

The Sweden Solar System is the world's largest permanent scale model of the Solar System. The Sun is represented by the Avicii Arena in Stockholm, the largest hemispherical building in the world.

Based on what you have read provide two positives and two negatives the Suarez family would face if they switch to organic farming

Answers

Hi, you did not enter the text about the Suarez family, which makes it impossible for this question to be answered accurately. However, from the context of your question, it is possible to see that you want to know two positive and negative points that the Suarez family would observe when starting a planting of organic agriculture.

Among the negative points, we can say that organic agriculture has a high cost, as the techniques used in it require a greater number of resources, which can make not only the service more expensive, but also the product. A second negative point is that the techniques used in organic agriculture are more difficult than the techniques used in conventional agriculture, since all management of organic crops must be carried out without the application of chemical products.

Among the positive points, we can say that the growing number of consumers of organic products can increase the profit that the family will have from the sale of these products. In addition, the family will have healthier, less polluted and more productive land.

Answer:

Sample response: Organic farming would have higher costs, and would be more complex than conventional farming. However, the Suarez family could charge a higher price for organic produce. This type of farming also would be better for the land.

Explanation:

The horizontal beam is supported by member DE and a uniform distributed load is applied as shown. Determine the internal loading at the location marked by the red line.

Answers

At the location marked by the red line, the total internal loading is -4 kN of shear force and 8 kNm of the moment.

The internal loading due to the support at the wall can be determined using the equation for the shear force (V) and the moment (M) at any point along the beam:

V = -wL/2 = -4*6/2 = -12 kN

M = 0 kNm

Next, we will determine the internal loading due to the uniform distributed load. The shear force (V) and the moment (M) at any point along the beam due to the uniform distributed load can be determined using the following equations:

V = wx = 42 = 8 kN

M = (wx)(x/2) = (42)(2/2) = 8 kNm

Finally, we will add the internal loading due to the support at the wall and the uniform distributed load to find the total internal loading at the location marked by the red line:

V_total = V_support + V_load = -12 + 8 = -4 kN

M_total = M_support + M_load = 0 + 8 = 8 kNm

So at the location marked by the red line, the total internal loading is -4 kN of shear force and 8 kNm of moment.

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The complete question is:

A horizontal beam of length L = 6 m is supported by a wall at one end and a uniform distributed load of w = 4 kN/m is applied to the beam along its entire length. The internal loading at the location marked by the red line, which is located at a distance x = 2 m from the left end of the beam, needs to be determined.

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1. A wave with a frequency of 10 Hz has a wavelength of 3 meters. At what
wave speed will this wave travel?

Answers

Answer:

30 m\ s Ans .....

Explanation:

Data:

f = 10 Hz

w = 3 m

v = ?

Formula:

v = fw

Solution:

v = ( 10)(3)

v = 30 m\ s Ans ........

Choose:-

The opposite table shows the relation between
the resultant force of two forces and
the angle between them then the values of the
two forces are
a) 4N,3N
b) 6N,5N
c)3N,2N
d)2N,1N


CAN ANYONE ANSWER ME PLZZ?? QUICKLY !

Choose:-The opposite table shows the relation betweenthe resultant force of two forces andthe angle between

Answers

My mommy wants to talk to you

How do adaptations help an animal survive?

Answers

Answer: Depends on their adaptions such as they may be able to change their color of their skin to camouflage to hide from predators or they are able to survive in harsh weather where they live in.

Explanation:

Answer: An adaptation is a very particular skill which helps an animal do the things they do in every day life .  Adaptation basically helps an animal survive in the environment they have decided to live in .

Hoped I helped -

Sleepy~

Whats 20 degrees South of West? (Vectors)

Answers

20 degrees South of West is 200° from the East in counter-clockwise direction.

The vector direction should always be described from the East in counter-clockwise direction. So,

0 degrees will be perfect East,45 degrees will be perfect North East 90 degrees will be perfect North,135 degrees will be perfect North West180 degrees will be perfect West225 degrees will be perfect South West270 degrees will be perfect South315 degrees will be perfect South East360 degrees will be perfect East which is also 0 degrees

If not mentioned in vector form, it can simply be described using two directions. Here it is given 20 degrees South of West. So, it lies in third quadrant. Up to west it is 180 degrees and 20 degrees South of West is given. So the vector direction is 180 + 20 = 200 degrees.

Therefore, 20 degrees South of West is 200°

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based on experiment 1 and 2, the viscosity of SAE 30 motor oil at 25°C is closest to which of the following

based on experiment 1 and 2, the viscosity of SAE 30 motor oil at 25C is closest to which of the following

Answers

Answer:

A. 30 cp. B. 60 cp. C. 200 cp. *D. 400 cp. 0

Answer:

It is 200 cp.

Explanation:

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the ________ waves advance in a backward-rotating, elliptical motion.

Answers

The Rayleigh Waves advance in a backward-rotating, elliptical motion.

Rayleigh waves, also known as ground roll or ground motion, are a type of surface wave that travels along the interface between a solid medium, such as the Earth's crust, and an adjacent fluid or semi-fluid medium, such as the atmosphere or water. These waves are named after Lord Rayleigh, who first mathematically described them in the late 19th century.

Rayleigh waves are formed as a result of the interaction between compressional (P) waves and shear (S) waves near the Earth's surface. When an earthquake or other seismic event occurs, P waves and S waves are generated and propagate through the Earth's interior. As they reach the surface, they give rise to Rayleigh waves, which travel along the surface of the Earth.

Rayleigh waves have a rolling or elliptical motion, similar to the motion of ocean waves, and they move in a retrograde elliptical path. The particles of the medium through which Rayleigh waves pass move both horizontally and vertically in elliptical orbits, gradually decreasing in amplitude with depth. The motion of Rayleigh waves is primarily vertical and perpendicular to the direction of wave propagation.

One important characteristic of Rayleigh waves is that they have a slower velocity compared to P and S waves. This results in a longer period of ground motion and causes Rayleigh waves to have a larger amplitude, making them particularly destructive near the epicenter of an earthquake.

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The magnetic field due to a long straight wire at a point near it is inversely proportional to the square of the distance from the wire. T/F

Answers

The statement that 'the magnetic field due to a long straight wire at a point near it is inversely proportional to the square of the distance from the wire' is true.

Is the statement true or false?

The statement is true. When an electric current flows through a long, straight wire, a magnetic field is produced around the wire. The strength of the magnetic field is directly proportional to the magnitude of the current flowing through the wire. Additionally, the magnetic field produced by the wire is inversely proportional to the distance from the wire squared.

This relationship can be expressed mathematically using the Biot-Savart law, which states that the magnetic field dB at a point P due to a current element dl is given by:

\(dB = μ0/4π * (Idl x r) / r^3\)

where I is the current in the wire, μ0 is the permeability of free space, r is the distance between the current element and the point P, and dl is the length of the current element.

Integrating the expression for dB over the entire length of the wire gives the total magnetic field B at point P. Since the magnetic field is proportional to \(1/r^2,\) as the distance from the wire increases, the magnetic field strength decreases rapidly.

In summary, the magnetic field produced by a long, straight wire is inversely proportional to the square of the distance from the wire. This relationship is essential in many applications, including the design of transformers and motors.

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