Question

A slab of insulating material of uniform thickness d, lying between -d/2 to +d/2 along the x axis, extends infinitely in the y and z directions. The slab has a uniform charge density rho. The electric field is zero in the middle of the slab, at x = 0.

(a) What is Eout, the magnitude of the electric field outside the slab? As implied by the fact that Eout is not given as a function of x this magnitude is constant everywhere outside the slab, not just at the surface. Express your answer in terms of d, rho, and ε_0.
(b)What is Ein, the magnitude of the electric field inside the slab as a function of x? Express your answer in terms of x, rho, and ε_0.

Answer 1

Answer: a) The electric field outside the slab can be calculated using Gauss's Law. Since the electric field is zero in the middle of the slab and the charge density is uniform, the electric flux through any Gaussian surface that encloses the middle of the slab will be zero. Therefore, the electric field outside the slab must also be zero.

b) Inside the slab, the electric field can be calculated using the formula for the electric field due to a uniform charge distribution: E = rho/(2*ε_0). This formula gives the electric field as a constant, independent of x. The electric field inside the slab will be uniform and directed from the negative charge towards the positive charge.