question_answer

The electric potential at a point \[(x,\ y)\] in the \[x-y\] plane is given by \[V=-kxy\]. The field intensity at a distance \[r\] from the origin varies as                                [UPSEAT 2002]

A)            \[{{r}^{2}}\]                          

B)            r

C)            \[\frac{1}{r}\]                      

D)            \[\frac{1}{{{r}^{2}}}\]

Correct Answer: B

Solution :

            \[{{E}_{x}}=-\frac{dV}{dx}=-\,ky\]; \[{{E}_{y}}=-\frac{dV}{dy}=\,-kx\] Þ \[E=\sqrt{E_{x}^{2}+E_{y}^{2}}=k\sqrt{{{x}^{2}}+{{y}^{2}}}=kr\]Þ E  µ r