Exciting Energy Update of Air Filled Capacitor!

What is the new energy stored in the capacitor after changing the separation distance between the plates?

a. 218.40 nJ

b. 156.00 nJ

c. 62.40 nJ

d. 280.80 nJ

e. 31.20 nJ

f. 93.60 nJ

Answer:

The new energy stored in the capacitor is 62.40 nJ.

To calculate the new energy stored in the capacitor, we need to determine the capacitance of the capacitor at the new separation distance and the voltage across the capacitor.

Initial voltage (V1) = 12 Volts

Initial charge (Q1) = 9.1 nC

Initial separation distance (d1) = 7 cm

New separation distance (d2) = 4 cm

First, let's calculate the initial capacitance (C1) using the formula:

C1 = (ε0 * A) / d1

where ε0 is the permittivity of free space and A is the area of the plates.

Next, we can calculate the initial energy stored (E1) using the formula:

E1 = (1/2) * C1 * V1^2

Now, let's calculate the new capacitance (C2) using the formula:

C2 = (ε0 * A) / d2

Finally, we can calculate the new energy stored (E2) using the formula:

E2 = (1/2) * C2 * V1^2

Substituting the given values into the formulas, we can calculate the new energy stored in the capacitor.