Question

Suppose a capacitor has an opposite net charge of magnitude 6.49 uC on its plates. If an electric field of magnitude 2.50 kV mm is needed between the plates, calculate the area of the plate (in m?). Enter your answer to within two decimal points. Use a period (full stop) for a decimal point. eg. 5.00- Do not use a comma or input your answer in some form of scientific notation. Do NOT include units in your answer.

Answer 1

To calculate the area of the plate, we can use the formula for the electric field between the plates of a capacitor:

Electric field (E) = Net charge (Q) / (ε₀ * Area)

where Q is the net charge on the plates and ε₀ is the permittivity of free space.

Rearranging the formula, we can solve for the area:

Area = Net charge / (Electric field * ε₀)

Given that the net charge is 6.49 uC and the electric field is 2.50 kV/mm, we need to convert these values to the appropriate units before plugging them into the formula.

1 uC = 10^-6 C
1 kV = 10^3 V
1 mm = 10^-3 m

So, the net charge becomes 6.49 * 10^-6 C and the electric field becomes 2.50 * 10^3 V/m.

Now we can calculate the area:

Area = (6.49 * 10^-6 C) / (2.50 * 10^3 V/m * ε₀)

The permittivity of free space, ε₀, is approximately 8.854 * 10^-12 F/m.

Substituting this value into the formula, we have:

Area = (6.49 * 10^-6 C) / (2.50 * 10^3 V/m * 8.854 * 10^-12 F/m)

Calculating this expression will give us the area of the plate in square meters.