Question

This animation shows a coaxial capacitor with cylindrical geometry: a very long cylinder (extending into and out of the page) in the center surrounded by a very long cylindrical shell (position is given in centimeters, electric field strength is given in newtons/coulomb, and electric potential is given in volts). The outside shell is grounded, while the inside shell is at 10 V. You can click-drag to measure the voltage at any position.

1. Use Gauss's law to show that the magnitude of the radial electric field between the two conductors for a cylindrical coaxial capacitor of length L is E = Q/2πrLε₀ = 2kQ/(rL), where Q is the total charge on the inside (or outside) conductor and r is the distance from the center.

2. Use V = -∫ E · dr to show that the potential at any point between the two conductors is V = (Q/2πLε₀) ln(b/r) = (2kQ/L) ln(b/r), where b is the radius of the outer conductor.

Answer 1

Kindly put, Q = lambda * L

and { (1/4π€) = k } to get the desired results