Question

A solid conducting sphere of radius 2.00 cm has a charge 11.00 µC. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a total charge of -1.00 µC. (Take radially outward as the positive direction.) (a) Find the electric field at r = 1.00 cm from the center of this charge configuration. MN/C (b) Find the electric field at r = 3.00 cm from the center of this charge configuration. MN/C (c) Find the electric field at r = 4.50 cm from the center of this charge configuration. MN/C (d) Find the electric field at r = 7.00 cm from the center of this charge configuration. MN/C

Answer 1

In case of radial symetry of charge distribution, electric field at distance r from the center,

E = kq/r^2.

q is the net charge inside sphere of radius r

Direction of field is radially outward if q is +ve and inward if q is -ve.

Electric field in the body of conductor is zero. Hence,

If distance r from center lies inside conductor, net charge inside sphere of radius r has to be zero.

To make field inside shell equal to zero, charge of -11 micro C is induced at inner surface of shell.

E1( 1cm from center) =0, as point lies inside conducting sphere.

E3 = k 11×10^-6 / 9×10^-4

= 110 MN/C. ( k = 9×10^9)

E4.5 = 0. (Point lies inside shell)

E7 = k 10×10^-6 / 49×10^-4. (Net charge inside sphere of radius 7 cm is 10 micro C)

E7 = 18.4 MN/C