AP Physics C E and M

Question

A capacitor is constructed of two large, identical, parallel metal plates separated by a small distance d. A battery fully charges the capacitor and is then disconnected.

If, instead of separating the plates, the empty space between the plates is filled with a slab of insulating material that has a dielectric constant κ= 2, which of the following correctly describes the change, if any, of the voltage across the capacitor, the electric field between the plates, and the energy stored in the capacitor?

1) Voltage halves

Electric field halves

Energy halves

2. Voltage halves

Electric field halves

Energy does not change

3. Voltage does not change

Electric field does not change

Energy halves

4. Voltage does not change

Electric field halves

Energy halves

5. Voltage does not change

Electric field does not change

Energy does not change

Answer 1

When a dielectric material is introduced between the plates, the material in the dielectric polarizes, producing charge separation that somewhat offsets the original electric field.

The resulting field, E, within the dielectric is the original field, Eo, divided by the dielectric constant, k.

The resulting voltage, V, due to this is the original voltage, Vo, divided by the dielectric constant, k.

Similarly, the stored energy, U, is the original energy, Uo, divided by the dielectric constant, k.

Thus, for k=2, the first answer is correct: V, E, and U are half the original values.