Question

The figure shows two nonconducting spherical shells fixed in place. Shell 1 has uniform surface charge density +5.2 μC/m2 on its outer surface and radius 3.6 cm , shell 2 has uniform surface charge density +3.1 μC/m2 on its outer surface and radius 1.9 cm; the shell centers are separated by L = 11.5 cm. what is the x-component (with sign) of the net electric field at x = 2.1 cm? Shell Shell

Answer 1

Consider the given data, The charge density of shell 1 is o, = +5.2.". The charge density of shell 2 is o2 = +3.1.“, Radius of shell 1 is R = 3.6 cm Radius of shell 2 is R = 1.9 cm The separation between the two shells is L=11.5 cm. From the figure, The point x = 2.1 cm lies inside the shell 1, so there is no charge is enclosed for any gaussian surface inside shell 1. Thus, the contribution of shell 1 to electric field at point x= 2.1cm is zero. The shell 2 behaves as a point charge at the center of 2nd shell: thus, the effective distance between the point and the charge is L-X

Therefore, the field points toward the negative x- direction. Ē = E(-a) kq-a ko,Ą (-as) (L - x) Here, A, is the area of shell 2 A2 = 41 R Ē – ko,40 R} (L - x)' (9x10°)(3.1x10“)47(1.9x10-2) (11.5x10-2 -2.1x10-2) = 1.432x10^(-a)