Question

An uncharged capacitor has parallel plates 5.0 cm on a side, spaced 1.2 mm apart.How much charge must be transferred between the initially uncharged plates in order to store 18 mJ of energy?

Answer 1

To find the charge required to store 18 mJ in a parallel-plate capacitor, calculate the capacitor's capacitance with the given dimensions and then apply the formula for energy stored in a capacitor.

Step-by-step explanation:

The question concerns a parallel-plate capacitor which has been charged in order to store a specific amount of energy. The amount of charge needed can be determined by using the energy stored in a capacitor formula: U = (1/2)CV^2, where U is the stored energy, C is the capacitance, and V is the voltage. The capacitance can be calculated using the formula for capacitance of a parallel-plate capacitor, C = ε_0(A/d), where ε_0 is the vacuum permittivity (8.85 ×10^{-12} F/m), A is the area of the plates, and d is the separation between the plates.

For the given measurements of the plates (5 cm on a side) and the space between them (1.2 mm), first find the capacitance C and then rearrange the energy equation to find the charge Q needed to store 18 mJ of energy, using the relationship Q = √(2UC).