Question

An uncharged capacitor has parallel plates 5.0 cm on a side, spaced 1.4 mm apart. How much charge must be transferred between the initially uncharged plates in order to store 15 m.J of energy?

Answer 1

To find the charge needed to store 15 mJ of energy in a capacitor, we first calculate the capacitance and then the voltage across the capacitor. Following these steps, we can determine the charge using the formula Q = CV.

Step-by-step explanation:

To calculate the charge that must be transferred to store 15 mJ (millijoules) of energy in a parallel-plate capacitor with given dimensions, we can use the formula for the energy (U) stored in a capacitor: U = (1/2)CV2, where C is the capacitance and V is the voltage across the plates.

First, we need to find the capacitance using the formula C = ε0A/d, where ε0 is the permittivity of free space (8.85 x 10-12 C2/N m2), A is the area of the plates, and d is the separation between them.

For a plate area of 5.0 cm on each side (0.05 m x 0.05 m) and a separation of 1.4 mm (0.0014 m), the capacitance (C) is found to be approximately 2.51 x 10-11 F (farads). Next, we solve for the voltage (V) across the plates using: U = (1/2)CV2. Having found V, we can then find the charge (Q) using Q = CV.

Through these steps, we can determine the amount of charge that needs to be transferred to store the specified energy.