question_answer

Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:

A non-conducting solid sphere of radius R is uniformly charged. The magnitude of the electric field due to the sphere at a distance r from its centre (1) increases as r increases for r < R (2) decreases as r increases for\[0<r<\infty \] (3) decreases as r increases for\[R<r<\infty \] (4) is discontinuous at\[r=R\]

A)   1, 2 and 3 are correct

B)  1 and 2 are correct

C)   2 and 4 are correct

D)  1 and 3 are correct

Correct Answer: D

Solution :

                 Inside the sphere \[E=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Q}{{{R}^{3}}}r\] \[E\propto r\]for \[r\le R\] i.e., E at centre = 0 as \[r=0\] and E at surface\[=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Q}{{{R}^{2}}}\] as\[r=R\] Outside the sphere \[E=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Q}{{{r}^{2}}}\]for\[r\ge R\]or\[E\propto \frac{1}{{{r}^{2}}}\] Thus, variation of electric field (E) with distance (r) from the centre will be shown