Question

A hollow, conducting sphere with an outer radius of .250 m and an inner radius of .200 m has a uniform surface charge density of -6.37 muC/me2.When a charge is now introduced at the center of the cavity inside the sphere, the new charge density on the outside of the sphere is -4.46 muC/me2. What is the charge at the center of the cavity?

Answer 1

Surface charge density on the outer sphere is - 6.37 C / m².

Radius of the outer sphere = 0.25 m.

Hence , surface area of the outer sphere = 4 x 0.25² m² = 0.785 m².

So, charge on the sphere was initially Q = - 6.37 C / m² x 0.785 m² = - 5 C.

Now, when a charge, say, q C, is kept into the cavity of the spherical shell, a - q C charge will be induced at the inner sphere, and + q C to the outer one.

Hence, net charge on the outer sphere becomes ( Q + q ) C = ( q - 5 ) C.

Hence, new charge density on the outside sphere becomes ( q - 5 ) C / 0.785 m².

According to the question,

( q - 5 ) / 0.785 = - 4.46

or, 5 - q = 4.46 x 0.785 = 3.5

or, q = 5 - 3.5 = + 1.5.

Hence, the charge at the center of the cavity is + 1.5 C.