At a distance of 0.220 cm from the axis of a very long charged conducting cylinder with radius 0.100cm, the electric field is 490 N/C . What is the electric field 0.616 cm from the axis of the cylinder?

At the distance of 0.220cm from the axis.

r = 0.220cm = 0.0022m, E = 490N/C, e0 = 8.854 x 10^-12F/m

Linear charge density = 2*π*e0*r*E = 2 x 3.142 x 8.854x10^-12 x 0.0022 x 490 = 5.998 x 10^-11C/m

Thus, To Calculate the Electric field at the distance r = 0.616cm from the cylinder axis, we substitute the calculated linear change density in the equation

E = (linear charge density)/2*π*e0*r

Here, r = 0.616cm = 0.00616m

E = [(5.998 x 10^-11)/(2 x 3.142 x 8.854 x 10-12 x 0.00616)]

E = 175N/C

Explanation:

The Electric field of a charged conducting cylinder obey the Gauss Law.

Therefore, the Electric field is given as:

E = (linear charge density)/4πe0r,

Where e0 is the permittivity of free space with constant value of 8.854 x 10^-12F/m, r is the radial distance from the axis.