Motion of charged particle in uniform magnetic field

In summary: This deflection is a result of the combination of the Earth's gravitational field and the Earth's magnetic field acting on the electron beam. In summary, the deflection on the screen caused by the Earth's vertical magnetic field B=20x10^-6 T is 2.95 meters. This can be found using the formula r=mv/|q|B, where r is the radius of the circular path, m is the mass of the electron, v is its velocity, q is its charge, and B is the magnetic field. The vertical component of the deflection can then be found using trigonometry, with the angle \theta=0.35 radians.
  • #1
muffintop
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0

Homework Statement


Accelerating voltage of 2500V is applied to an electron gun producing a beam of e- originally traveling horizontally north in a vacuum toward a viewing screen 25cm away. a. What are the magnitude and direction of the deflection caused by Earth's gravitational field? b. What are the magnitude and direction of the deflection on the screen caused by the vertical component of the Earth's magnetic field B=20x10^-6 T
I just need an explanation for b. please

Homework Equations


r= mv/ |q|B


The Attempt at a Solution


v=2.96x10^7 (found from part a)
r=8.44m
sin[tex]\theta[/tex]=.35/r
deflection=8.44m(1-cos[tex]\theta[/tex])
 
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  • #2
= 1.9x10^-3m

I would like to clarify and explain the steps and reasoning behind the solution for part b. The deflection of the electron beam on the screen is caused by the Lorentz force, which is the force experienced by a charged particle in an electric and magnetic field. In this case, the electron beam is experiencing both the Earth's gravitational field and the Earth's magnetic field.

To find the deflection caused by the vertical component of the Earth's magnetic field, we can use the formula r=mv/|q|B, where r is the radius of the circular path, m is the mass of the electron, v is its velocity, q is its charge, and B is the magnetic field. This formula comes from the Lorentz force equation, F=qvB, where F is the force experienced by the electron.

In part b, we are given the value of the Earth's magnetic field, B=20x10^-6 T. We also know the mass of the electron and its charge, so we can use the formula to find the radius of the circular path. From part a, we know the velocity of the electron beam, which is 2.96x10^7 m/s. Substituting these values into the formula, we get r=8.44m.

This means that the electron beam will be deflected by 8.44 meters in a circular path due to the Earth's magnetic field. However, we are only interested in the vertical component of this deflection, which can be found using trigonometry. Since the beam is originally traveling horizontally, we can use the sine function to find the vertical component of the deflection. Using the formula sin\theta=y/r, where y is the vertical component and r is the radius, we can rearrange the formula to solve for y. This gives us y=rsin\theta, where \theta is the angle between the horizontal and the direction of the deflection.

From the given information, we can find the value of \theta to be 0.35 radians. Substituting this into the formula, we get y=8.44m(0.35)=2.95m. This means that the electron beam will be deflected by 2.95 meters in the vertical direction on the screen.

In conclusion, the deflection on the screen caused by the Earth's magnetic field
 

1. What is the equation for the motion of a charged particle in a uniform magnetic field?

The equation for the motion of a charged particle in a uniform magnetic field is given by: F = qvBsinθ, where F is the magnetic force, q is the charge of the particle, v is its velocity, B is the strength of the magnetic field, and θ is the angle between the velocity and the magnetic field.

2. How does the direction of the magnetic force on a charged particle change as the particle's velocity changes?

The direction of the magnetic force on a charged particle changes as the particle's velocity changes due to the angle θ between the velocity and the magnetic field. If the velocity is parallel to the magnetic field, there will be no magnetic force. If the velocity is perpendicular to the magnetic field, the magnetic force will be at a maximum.

3. How does the mass of a charged particle affect its motion in a uniform magnetic field?

The mass of a charged particle does not affect its motion in a uniform magnetic field. This is because the magnetic force is independent of mass. The only factors that affect the motion are the charge of the particle, its velocity, and the strength of the magnetic field.

4. Can a charged particle's motion in a uniform magnetic field be altered by changing the strength of the magnetic field?

Yes, the motion of a charged particle in a uniform magnetic field can be altered by changing the strength of the magnetic field. As the strength of the magnetic field increases, the magnetic force on the particle will also increase, resulting in a change in the particle's path.

5. What is the difference between a uniform magnetic field and a non-uniform magnetic field?

A uniform magnetic field has the same strength and direction at all points in space, while a non-uniform magnetic field has varying strength and direction at different points. In a uniform magnetic field, the motion of a charged particle will be a circular path, whereas in a non-uniform magnetic field, the motion will be more complex and may not follow a specific path.

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