### All AP Physics C: Mechanics Resources

## Example Questions

### Example Question #1 : Magnetism

A proton traveling enters a uniform magnetic field and experiences a magnetic force, causing it to travel in a circular path. Taking the magnetic field to be , what is the radius of this circular path (shown in red)?

**Possible Answers:**

**Correct answer:**

To calculate the magnetic force of a single charge, we use , where is the charge of the proton, is its velocity, is the uniform magnetic field.

Since this magnetic force causes the proton to travel in a circular path, we set this magnetic force equation equal to the centripetal force equation.

is the mass of the proton and is the radius of the circular path. Solve for .

Using the values given in the question, we can solve for the radius.

### Example Question #1 : Magnetism

Which of the following best describes the net magnetic flux through a closed sphere, in the presence of a magnet?

**Possible Answers:**

Zero regardless of the orientation of the magnet

Negative only if the north pole of the magnet is within the surface

More than one of the other options is true

Positive only if the north pole of the magnet is within the surface

Zero only if the magnet is completely enclosed within the surface

**Correct answer:**

Zero regardless of the orientation of the magnet

The net magnetic flux (or net field flowing in and out) through any closed surface must always be zero. This is because magnetic field lines have no starting or ending points, so any field line going into the surface must also come out. In other words, "there are no magnetic monopoles."

### Example Question #1 : Understanding Magnetic Fields And Charges

A particle of charge and mass moves with a speed of perpendicular to a uniform magnetic field, . What is the period of the particle's orbit in the field?

**Possible Answers:**

**Correct answer:**

Relevant equations:

Set the magnetic force equal to the centripetal force, since the magnetic force is directed towards the center of the particle's circular path and centripetal force is defined as the net force towards the center of a circular path.

Rearrange to isolate the velocity:

Determine the distance, , traveled in one revolution, which is the circumference of a circle of radius :

Plug this distance and velocity into , to solve for the period :

### Example Question #1 : Understanding Magnetic Fields And Charges

Consider a current-carrying loop with current , radius , and center .

A particle with charge flies through the center and into the page with velocity . What is the total electromagnetic force on the particle at the instant that it flies through the loop, in terms of the variables given?

**Possible Answers:**

**Correct answer:**

The correct answer is zero. To calculate the force of a magnetic field on a moving charged particle, we use the cross product. We know that if the magnetic field is parallel to the velocity vector of the particle, then the force produced is zero.

Because our magnetic field in this case is going in the same direction as the velocity of the particle, we know that the magnetic force on the particle is zero.

### Example Question #1 : Understanding Magnetic Fields And Charges

Consider two long, straight, current-carrying wires at distance from each other, each with a current of magnitude going in opposite directions.

If the two wires described are not held in place, what motion will result from the magnetic fields produced?

**Possible Answers:**

The wires will remain in place

The wires will rotate clockwise

The wires will move away from each other

The wires will rotate counterclockwise

The wires will move toward each other

**Correct answer:**

The wires will move away from each other

The answer is that the wires will move from each other. Using our right hand rule, we know that the magnetic fields produced by each wire are in the same direction, as long as their currents oppose. Using the right hand rule again to determine the direction of the force exerted on each wire by the magnetic field with which they are interacting yields a force in the direction away from the other wire for each wire.

### Example Question #1 : Magnetism

Two infinitely long wires having currents and are separated by a distance .

The current ** **is 6A into the page. The current ** **is 9A into the page. The distance of separation is 1.5mm. The point lies 1.5mm away from on a line connecting the centers of the two wires.

What is the magnitude and direction of the net magnetic field at the point ?

**Possible Answers:**

**Correct answer:**

At point , the magnetic field due to points right (via the right hand rule) with a magnitude given by:

At point , the magnetic field due to points right (via the right hand rule) with a magnitude given by:

The addition of these two vectors, both pointing in the same direction, results in a net magnetic field vector of magnitude to the right.

### Example Question #1 : Magnetism

Consider a current-carrying loop with current , radius , and center .

What is the direction of the magnetic field produced?

**Possible Answers:**

Into the screen

There is no resultant magnetic field

Counterclockwise

Clockwise

Out of the screen

**Correct answer:**

Into the screen

The correct answer is into the page. As the current is moving clockwise, we can use our right hand rule for magnetic fields produced by a current-carrying loop. Curl the fingers of your right hand in the direction of the current. This should result in your thumb pointing toward the screen, indicating the direction of the magnetic field.

### Example Question #1 : Understanding Magnetic Fields And Wires

Consider a current-carrying loop with current , radius , and center .

What would happen to the magnetic field at point if the radius was halved and current was multiplied by four?

**Possible Answers:**

The new magnetic field would be eight times weaker than the original

The new magnetic field would be four times as strong as the original

The new magnetic field would reverse direction

The new magnetic field would be eight times as strong as the original

The new magnetic field would be four times weaker than the original

**Correct answer:**

The new magnetic field would be eight times as strong as the original

The current flowing clockwise through the wire will induce a magentic field directed into the screen. The magnitude of such a magnetic field is given by the equation:

Using out altered values, we can derive a ratio to determine the change in magnetic field.

The resulting field will be eight times stronger than the original.

### Example Question #41 : Electricity And Magnetism Exam

Consider a current-carrying loop with current , radius , and center .

What is the magnitude of the magnetic field at point ?

**Possible Answers:**

There is no magnetic field at point

**Correct answer:**

The current flowing clockwise through the wire will induce a magentic field directed into the screen. The magnitude of such a magnetic field is given by the equation:

### Example Question #41 : Electricity And Magnetism Exam

Consider two long, straight, current-carrying wires at distance from each other, each with a current of magnitude going in opposite directions.

What is the magnitude of the magnetic field at a point equidistant from both wires?

**Possible Answers:**

Zero

**Correct answer:**

Using our right hand rule for magnetic fields produced by current-carrying wires, we know that the magnetic field produced by each wire is in the same direction within the distance between the wires. Therefore, we know that the total magnetic field is simply the magnetic field of one of the wires multiplied by two.

Use the equation for magnetic field:

Multiply by two, since the magnetic field will be equal for each wire, and substitute the given variables: