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            \[E\propto \frac{1}{{{R}^{2}}}\]                                 ?(iii) 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: