Question

The electric field at 5 cm from the center of a long copper rod of radius 2 cm has a magnitude of 5 N/C and is directed outward from the axis of the rod.

(a)

How much charge per unit length (in C/m) exists on the copper rod?

C/m

(b)

What would be the electric flux (in N · m²/C) through a cube of side 5 cm situated such that the rod passes through opposite sides of the cube perpendicularly?

N · m²/C

Answer 1

Part A.

For a cylindrical rod, electric field on the axis of rod is given by:

E = 2*k*/r

= Charge per unit length = ?

E = 5 N/C

k = 9*10^9

r = electric field at 5 cm from the center of rod = 5 cm = 0.05 m

So,

= E*r/(2*k)

= 5*0.05/(2*9*10^9)

= 1.39*10^-11 C/m = Charge per unit length

Part B.

Electric flux according to gauss's law is given by:

Qenc = Charge inside gaussian surface = Charge per unit length of copper rod*length of cube = *L

Qenc = 1.39*10^-11*0.05

e0 = 8.85*10^-12

So,

= 1.39*10^-11*0.05/(8.85*10^-12)

= Electric flux = 0.079 N.m^2/C

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