question_answer

Which of the following plots represents the variation of the electric field with distance from the centre of a uniformly charged non- conducting sphere of radius R?

A)   

B)  

C)  

D)  

Correct Answer: D

Solution :

The electric field intensity at a point lying outside the sphere (non-conducting) is                 \[E=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{{{r}^{2}}}\] where r is the distance of that point from centre of sphere.                 \[\therefore \] \[E\propto \frac{1}{{{r}^{2}}}\] ... (i) The electric field intensity at surface of sphere                 \[E=\frac{q}{4\pi {{\varepsilon }_{0}}{{R}^{2}}}\] or            \[E\propto \frac{1}{{{R}^{2}}}\] ... (ii) R, being the radius of sphere. The electric field intensity at a point lying inside the sphere is                 \[E=\frac{qr}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}\] or            \[E\propto r\] ... (iii) Also at the centre of sphere r = 0. Hence, E = 0. The graphical distribution is shown below: