# AP Physics 2 : Induction

## Example Questions

### Example Question #41 : Electricity And Magnetism

Suppose the induced electromotive force of a double loop wire has a magnitude of  when the change in magnetic flux is . How much time has elapsed for the flux change?

Explanation:

Write the formula for induced electromotive force.

Since there are two loops, .

Solve for .

### Example Question #1 : Induction

A magnetic rod is inside a coil of wire which is connected to an ammeter. If the rod is stationary, which of the following statements are true?

None of these

The rod loses its magnetic field

There is induced current relative to the strength of the rod's magnetic field

The rod induces a small current

There is no induced current

There is no induced current

Explanation:

Current is induced in wire when the magnetic flux changes. When the magnetic rod is in motion, the flux is changing, so current is induced. If the coil were expanded or contracted with the rod still there, the flux would change and current would be induced. In our case, the rod is stationary and the coil isn't changing shape. Therefore, the flux is not changing, so there is no current being induced. Additionally, there's no reason for the rod to lose its magnetic property.

### Example Question #3 : Induction

A system consists of two rails, whose resistance is zero, a conductive bar, whose resistance is also zero, and a resistor whose resistance, 0.02 Ohms. The bar remains in contact with the rails as it slides to the right with a velocity . The distance from one rail to the other is 0.07m. The magnetic field, which is directed out of the page, has a magnitude of 0.0015T. What is the magnitude and direction of current in the resistor?

No current will flow in the resistor

down toward the bottom of the page

down toward the bottom of the page

up toward the top of the page

up toward the top of the page

down toward the bottom of the page

Explanation:

When a conductor moves through a magnetic field in such a way that it cuts through magnetic field lines, the mobile charge carriers separate due to the magnetic force on them, creating a potential . Since there is no resistance anywhere else in the circuit, all of this potential is lost in the resistor, so we can apply Ohm's law:

Because the positive charge in the rod feels an upward force due to the right-hand rule, the top of the rod has a greater potential than the bottom, and current flows counterclockwise around the circuit, resulting in a downward direction in the resistor.

### Example Question #51 : Magnetism And Electromagnetism

resistor is connected to a coil with  turns and a cross sectional area of . A magnet is lowered as shown in the figure. The magnetic field increases from  to  in . Find the magnitude of the current going through the resistor.

Explanation:

There is a change in flux produced by the changing magnetic field which is given by

where  is the cross sectional area of the coil,  is the change in magnetic field, and  is the angle of the field lines relative to the normal of the cross section of the coil.

In this case the magnet is perpendicular to the cross section of the coil and so

The change in magnetic field is just the final given value minus the intial value. Faraday's Law says that an emf will be generated by a change in flux,

where  is the number of turns in the coil. Plugging in the change in flux gives

The change in time is just  since we can start our clock at zero. The current can be found using Ohm's Law where