A long insulating cylinder L meters long has a net charge of Q uniformly distributed throughout its volume. The radius of the cylinder is R. Consider a small cylindrical Gaussian surface inside the insulator and far from the ends of the insulator that is centred along the insulating cylinder's axis. The radius of the Gaussian surface is r < R and its length is d. (a) Write an expression for the charge inside the Gaussian surface, Qinside, in terms of r, d, R, L and Q. (b) Apply the Gauss's Law to write an expression for the electric field, E, inside the insulating cylinder at a point r meters from the axis. The expression for the electric field, E, should be in terms of Q, ɛ0, r, R, 2n, and L.

A long insulating cylinder L meters long has a net charge of Q uniformly distributed throughout its volume. The radius of the cylinder is R. Consider a small cylindrical Gaussian surface inside the insulator and far from the ends of the insulator that is centred along the insulating cylinder's axis. The radius of the Gaussian surface is r < R and its length is d. (a) Write an expression for the charge inside the Gaussian surface, Qinside, in terms of r, d, R, L and Q. (b) Apply the Gauss's Law to write an expression for the electric field, E, inside the insulating cylinder at a point r meters from the axis. The expression for the electric field, E, should be in terms of Q, ɛ0, r, R, 2n, and L.