question_answer

A solid metallic sphere has a charge + 3Q. Concentric with this sphere is a conducting spherical shell having charge - Q. The radius of the sphere is a and that of the spherical shell is\[b(b>a)\]. What is the electric field at a distance \[R(a<R<b)\] from the centre?

A)  \[\frac{4Q}{2\pi \,{{\varepsilon }_{0}}{{R}^{2}}}\]

B)  \[\frac{3Q}{4\pi \,{{\varepsilon }_{0}}{{R}^{2}}}\]

C)  \[\frac{3Q}{2\pi \,{{\varepsilon }_{0}}{{R}^{2}}}\]

D)  \[\frac{Q}{2\pi \,{{\varepsilon }_{0}}R}\]

Correct Answer: B

Solution :

The electric field inside a spherical charge is everywhere zero, that is \[E=0\] But point P is outside the inner sphere, hence for a point very close to the surface the intensity of electric field is given by                 \[E=\frac{1}{4\pi \,{{\varepsilon }_{0}}}\frac{q}{{{R}^{2}}}\] Given,   \[q=+3Q\] Therefore, \[E=\frac{1}{4\pi \,{{\varepsilon }_{0}}}\frac{3\,Q}{{{R}^{2}}}\]