Into the gap between the plates of a parallel plate capacitor of capacitance
A slab of metal is inserted halfway between the plates filling one fourth of the gap between the plates.What is the resulting new capacitance?

Question

Into the gap between the plates of a parallel plate capacitor of capacitance 
A slab of metal is inserted halfway between the plates filling one fourth of the gap between the plates.What is the resulting new capacitance?

Quizplus · Accepted Answer

The capacitance of a parallel plate capacitor is given by the formula C = εA/d, where ε is the permittivity of the material between the plates, A is the area of the plates, and d is the distance between the plates.

Since the slab is inserted halfway between the plates, it reduces the distance between the plates to d/2. The new distance between the plates is therefore (3/4)d. The area of the plates and the permittivity of the material between them remain the same. Thus, the new capacitance is:

C' = εA/(3/4)d = (4/3)εA/d

The capacitance has increased by a factor of 4/3. Therefore, the new capacitance is 11ea7ff9_2bed_0825_a768_e5894ea6ffb4_TB2295_11, which is choice B.

Into the Gap Between the Plates of a Parallel Plate