Question

2. Derive an expression for electric Field due to a Charged infinite plane sheet.​

Answer 1

Answer:

123

Explanation:

Answer 2

Answer:

E = sigma/(2×epsilon_0)

Explanation:

please see the enclosed attachment for detailed explanation and step by step working.

Let us treat the infinitely charged sheet as a combination of infinite number of concentric rings. of radius r and thickness dr, Let's say the area charge density be sigma Coul/m^2.

K = 1/(4π epsilon_0)

Electric field dE1 due to a small area dA

= r d phi × dr is = K sigma r d phi dr /(d^2 Sec^2 theta)

Electric field dE due to dE1 & dE2 along the axis of the ring

= 2 K sigma r dr Cos^2 theta /d^2

Electric field dE due to the thin ring of radius r and thickness dr at a point P which is at a distance d from the sheet

= 2πK sigma r dr Cos^2 theta /d^2

now r = d tan theta. dr = d sec^2 theta d theta.

dE = [sigma/(2 epsilon_0)] × Sin theta d theta.

Integrating dE over r =0 to infty, theta from 0 to π/2,

E = sigma/(2 epsilon_0)

It's independent of the distance d between the charged sheet and the point P.