A solid metal sphere of radius $a$ is carrying a charge +q. It is surrounded by a concentric uncharged metal shell of inner radius b and outer radius c. Choose the only wrong statement from the following.

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An Electric field is $\frac{q}{4 π \in_{0} r^{2}}$ for points lying between a and b.

An electric field is $\frac{q}{2 π \in^{0} r^{2}}$ at points for which $r > c .$

An electric field is zero for points lying between b and c.

The electric field is zero at points for which $r < a$ .

answer is D.

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Detailed Solution

At points for which $r < a$ , the electric field is zero because there can be no electric field within the body of a conductor.

At points for which $r$ lies between b and c, the inner sphere acts as if all its charge were concentrated at its center. Hence $E = \frac{q}{4 π ϵ_{0} r^{2}}$ .

At points for which r lies between b and c, the electric field is again zero because these points are in the body of a conductor.

The charge +q on the inner sphere induces a charge - q on the inner surface of the outer sphere and a charge +q on the outer surface of the outer sphere. At points for which r > c, the net charge enclosed inside the Gaussian spherical surface of radius r (> c) is $+ q + (- q) + (+ q) = + q .$ So the electric field for r > c is $E = \frac{q}{4 π ϵ_{0} r^{2}}$ .