# AP Physics 2 : Magnetic Force

## Example Questions

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### Example Question #1 : Magnetic Force

A particle with a charge of  is moving at perpendicularly through a magnetic field with a strength of . What is the magnitude of the force on the particle?

There is no force on the particle

Explanation:

The equation for finding the force on a moving charged particle in a magnetic field is as follows:

Here,  is the force in Newtons,  is the charge in Coulombs,  is the velocity in , and  is the magnetic field strength in Teslas.

Another way to write the equation without the cross-product is as follows:

Here,  is the angle between the particles velocity and the magnetic field.

For our problem, because theta is  evaluates to 1, so we just need to perform multiplication.

Therefore, the force on the particle is 0.3N.

### Example Question #2 : Magnetic Force

An  wire with a current of  is oriented  from parallel to a magnetic field with a strength of . What is the force on the wire?

The wire doesn't experience any force

Explanation:

The equation for the force on a current carrying wire in a magnetic field is as follows:

is the force in Newtons,  is the current in amperes,  is the magnetic field strength in Teslas, and  is the angle from parallel to the magnetic field.

Because our wire is not fully perpendicular to the magnetic field, it does not experience the full possible force. Instead, it experiences  times the maximum force value.

### Example Question #3 : Magnetic Force

A proton traveling at  in a horizontal plane passes through an opening into a mass spectrometer with a uniform  magnetic field directed upward. The particle then moves in a circular path through  and crashes into the wall of the spectrometer adjacent to the entrance opening. How far down from the entrance is the proton when it crashes into the wall?

The proton’s mass is  and its electric charge is .

Explanation:

A charged particle moving through a perpendicular magnetic field feels a Lorentz force equal to the formula:

is the charge,  is the particle speed, and  is the magnetic field strength. This force is always directed perpendicular to the particle’s direction of travel at that moment, and thus acts as a centripetal force. This force is also given by the equation:

We can set these two equations equal to one another, allowing us to solve for the radius of the arc.

Once the particle travels through a semicircle, it is laterally one diameter in distance from where is started (i.e. twice the radius of the circle).

Twice this value is the lateral offset of its crash point from the entrance:

### Example Question #1 : Magnetic Force

What is the force experienced by a  charge moving at  through a magnetic field with strength  at  from perpendicular to the field?

There is no net force on the charge

Explanation:

To find the force experienced by the charge, we use this equation:

Because the charge is moving at an angle from perpendicular, we need to take the cross product into account.

Theta is the angle from perpendicular, which is . Plug in known values and solve.

### Example Question #4 : Magnetic Force

An  charge is moving through a  magnetic field at a speed of  perpendicular to the direction of the field. What is the force on the charge?

There is no force on the charge

Explanation:

The equation for force on a charge moving through a magnetic field is:

Because the velocity is perpendicular to the field, the cross product doesn't matter, and we can do simple multiplication.

Therefore, the force on the charge is

### Example Question #5 : Magnetic Force

charge is moving through a  magnetic field at a speed of  from parallel to the magnetic field. What is the force on the charge?

The charge experiences no force

Explanation:

The equation for force on a charge moving through a magnetic field is:

.

The cross product is:

Above,  is the degree from parallel the charge is moving. The charge is moving at  from parallel, so the equation, once we plug in our numbers, is:

The force on the charge is about .

### Example Question #2 : Magnetic Force

A particle is moving parallel to a uniform magnetic field. Which of the following statements are true?

The particle experiences the most force possible in the setup

The particle has no net charge

None of the other statements are certain

The magnetic field is exerting no force on the particle

The particle will rotate around a point in the magnetic field

The magnetic field is exerting no force on the particle

Explanation:

The force experienced by a charged particle in a magnetic field is

This means that when a charge particle is moving perpendicular to the field, due to the cross-product, it experiences the most amount of force (because  is equal to , and theta equals  when it's perpendicular). This means that the charged particle will experience no force due to the magnetic field when it's parallel. We know there will be no force on the particle, and we also know that uncharged particles experience no force in magnetic fields, but we can't say for certain the particle has no net charge, only being told that it's moving parallel to the field.

### Example Question #7 : Magnetic Force

A rail system is formed in a magnetic field directed out of the page as diagrammed above. The rod remains in contact with the rails with zero friction as it moves to the right at a constant velocity of  due to an external force. The distance from one rail to the other is 0.087m. The rails and the rod have no resistance, but the resistor has a resistance of 0.0055 Ohms. The magnetic field has a magnitude of 0.035T. What is the magnitude and direction of the external force required to keep the rod moving at a constant velocity?

to the right

to the left

to the left

to the right

No force is necessary since the rod is moving at a constant velocity

to the right

Explanation:

The rod acts as a battery due to its motion in the magnetic field: . Because there is a closed circuit, this results in current flow:

In this simple circuit, the current is the same everywhere, so the same current flows through the rod. Because of this current, the rod feels a force:

By the right-hand rule, this magnetic force is directed to the left, so the external force must be directed to the right. It is interesting to note that the power dissipated in the resistor:

is the same as the power provided by the outside force:

The universe conspires to conserve energy.

### Example Question #3 : Magnetic Force

If a 10C charged particle is traveling perpendicularly to a magnetic field of 5T at a speed of , what is the force experienced by this charged particle?

Explanation:

This question is presenting us with a scenario in which a charged particle is traveling with a certain velocity through a magnetic field. In this situation, we're being asked to determine what the force experienced by this particle is.

To solve this question, we'll need to determine what kind of force this particle is likely to experience. Since we're told that the particle is traveling in a magnetic field, it would make sense that this particle is going to be affected by a magnetic force. Thus, we'll need to use the equation for magnetic force.

Moreover, since we're told in the question stem that this particle is traveling perpendicularly to the magnetic field, we know that  and thus . This helps reduce the equation down.

Now, all we need to do is plug in the values given to us in order to calculate the resulting force.

### Example Question #4 : Magnetic Force

A charged particle, Q, is traveling along a magnetic field, B, with speed v. What is the magnitude of the force the particle experiences?

Zero

Zero

Explanation:

Charged particles only experience a magnetic force when some component of their velocity is perpendicular to the magnetic field. Here, the velocity is parallel to the magnetic field so the particle does not experience a force.

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