The electric field must be zero inside a conductor in electr

The electric field must be zero inside a conductor in electrostatic equilibrium, but not inside an insulator. It turns out that we can still apply Gauss\'s law to a Gaussian surface that is entirely within an insulator by replacing the right-hand side of Gauss\'s law, Qin/0, with Qin/ , where is the permittivity of the material. (Technically, 0 is called the vacuum permittivity.) Suppose a long, straight wire with linear charge density 250 nC/mis covered with insulation whose permittivity is 2.50.

What is the electric field strength at a point inside the insulation that is 1.0 mmfrom the axis of the wire?

Solution

By Gauss’s law,

E.dA = Q_in/

Simplifying,

E= Q_in/(.dA)

dA= 2rL

Q_in = L

Thus,

E= L/(2rL)

E= /(2r)

Plugging given data,

E= (250*10^-9C/m)/(2*3.14*1.0*10^-3*2.50*8.85*10^-12)

E = 1.8*10^6 N/C