Question

a paraellel plate capacitor consists of 2 large circular sheets of metal separated by 1.53 cm. The electric field energy density betwwen plates is 4.41 J/m3 while the capacitor holds .127 J of potential energy. What is the radius of the circular platyes?

Answer 1

Answer:

The radius of the circular plate is 0.774 m

Explanation:

Given;

distance between the parallel plates, d = 1.53 cm = 0.0153 m

electric field energy density between plates, $U_E$  = 4.41 J/m³

Potential energy of the capacitor, $U_c$ = 0.127 J

Energy density is given as;

$U_E = \frac{U_c}{V}$

where;

V is volume

$V = \frac{U_c}{U_E} = \frac{0.127}{4.41} = 0.0288 \ m^3$

Volume is given as;

V = Ad

where;

A is area

A = V / d

A = (0.0288) / (0.0153)

A = 1.882 m²

Area of circular plate is given as;

A = πr²

where;

r is the radius of the circular plate

$r = \sqrt{\frac{A}{\pi} } \\\\r = \sqrt{\frac{1.882}{\pi}}\\\\r = 0.774 \ m$

Therefore, the radius of the circular plate is 0.774 m