question_answer

In the given figure, the electric lines of forces shaped like arcs of concentric circles with their centre at point O in the certain confined region of a field \[[a<r<b],\] where r is the radius of concentric arcs. The intensity of electric field in this section should be

A) Directly proportional to distance from \[O\]              

B) Directly proportional to square of distance from \[O\]

C) Inversely proportional to distance from \[O\]     

D) Inversely proportional to square of distance from \[O\]

Correct Answer: C

Solution :

   [c]         \[\oint{\vec{E}.\overrightarrow{dl}}\] along ABDCA \[{{E}_{1}}R\alpha -{{E}_{2}}r\alpha =0\] \[\Rightarrow \,\,\,{{E}_{1}}R={{E}_{2}}r\,\,\,\,\,\,\Rightarrow E\propto \frac{1}{R}\]