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## Example Questions

### Example Question #1 : Magnetic Forces And Energy

An electron is traveling at constant velocity directed to the the left through a magnetic field directed into the page as shown below.

Which way would the force vector on the electron due to the magnetic field be directed?

**Possible Answers:**

Towards the bottom of the page

Out of the page

Towards the right of the page

Towards the top of the page

**Correct answer:**

Towards the top of the page

When finding the direction of the force on a POSITIVELY charged particle due to a magnetic field, we can use the right hand rule. Holding your thumb perpendicular to the rest of your fingers (as if motioning to stop), orient your fingers parallel to the lines of the magnetic field, and your thumb with the velocity vector of the charge. For a positive charge, the force would be oriented directly out of the palm; HOWEVER, the charge of an electron is negative and therefore the force will be applied in the opposite direction. This would mean that the force would be coming directly out of the backside of your hand (in this case, towards the top of the page) using the right hand rule.

### Example Question #2 : Magnetic Forces And Energy

A charged particle enters a uniform magnetic field, with velocity v perpendicular to the field, and moves in a circular path of radius R. If the particle's mass were doubled, the radius would become __________.

**Possible Answers:**

4R

R

R/4

R/2

2R

**Correct answer:**

2R

A charged particle's motion in a uniform magnetic field is described by R = mv/qB, so the radius of the particle's path is proportional to its mass. Thus if mass is doubled, radius is also doubled.

### Example Question #4 : Magnetism And Electromagnetism

An electron is moving at a constant velocity due east. It travels from a region of zero magnetic field into a uniform magnetic field of nonzero magnitude and unknown direction. Which of the following could not describe the electron's motion after entering the field?

**Possible Answers:**

Its path begins curving to the north

Its path begins curving to the south

It continues traveling east at the same velocity

It continues traveling east, but at a greater velocity

It travels in a helical path

**Correct answer:**

It continues traveling east, but at a greater velocity

A magnetic force can accelerate a charged particle by changing the direction of its velocity, but cannot change the magnitude of velocity.

If the magnetic field has any components perpendicular to the particle's initial velocity, the particle will experience a force according to the equation:

This force is generated perpendicular to the particle's path and will cause a change in the direction of the particle's velocity. If the magnetic field is parallel to the initial velocity, the particle will experience no magnetic force, and its path will remain unchanged. It is not possible for the particle to accelerate in the magnetic field without changing direction.

### Example Question #2 : Magnetic Forces And Energy

What is the magnitude of force on a charge travelling at a constant velocity of through a perpendicular magnetic field?

**Possible Answers:**

**Correct answer:**

The equation for finding the force on a charge in a magnetic field is

*F = qvBsinθ *

Where q is charge in coulombs, v is the velocity of the charge, and B is the strength of the magnetic field in Teslas. Since the charge is moving perpendicular to the magnetic field, sinθ =1. Therefore we solve for force by plugging in the values and multiplying.

### Example Question #3 : Magnetic Forces And Energy

In a current-carrying wire, which of the following expressions best relates charge, current, velocity and the length of the wire?

Assume is 90^{o}.

**Possible Answers:**

**Correct answer:**

The force of a charge in a magnetic field is given by the equation . *q* is the charge, *v* is the velocity, and *B* is the magnetic field strength.

Additionally, the force on a current-carrying carrying wire in a magnetic field is given by the equation . *I* is the current, *L* is the length or the wire, and *B* is the magnetic field strength.

Because we assume the angle to be 90^{o }, we can set the two force equations equal to each other, and derive the equation .

By manipulating the variables, we can generate the equation . None of the other answer choices can be derived from these equations.

### Example Question #4 : Magnetic Forces And Energy

The particle depicted above on the left has a charge of and a velocity going to the right. What will happen when the particle enters the magnetic field depicted?

**Possible Answers:**

It will move downwards

It will move toward the observer

It will slow to a halt

It will move away from the observer

It will move upwards

**Correct answer:**

It will move away from the observer

To determine the direction the charge will accelerate, use the right hand rule for magnetic force. To begin, hold out your hand and give a "thumb up," now rotate your wrist clockwise so that your thumb is in the direction of the velocity of the charge. Next, extend your index finger so you are pointing into the plane of the page/screen with it, with your palm facing up. Now rotate your wrist so your index finger points in the direction of the magnetic field lines. Now your index finger should be pointing down, with your palm facing the screen/page, and your thumb still pointing to the right. The direction of the magnetic force felt by a positive charge is perpendicularly from your palm outwards, into the plane of the page/screen. Note that if the charge were negative, the direction of the magnetic force felt by the charge would be coming perpendicularly from the top of your hand instead.

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