question_answer

What is angle between electric field and equipotential surface?

A)  \[90{}^\circ \text{ }always\]      

B)        \[0{}^\circ \text{ }always\]

C) \[0{}^\circ \text{ }to\text{ }90{}^\circ \]                

D)        \[0{}^\circ \text{ }to\text{ }180{}^\circ \]

Correct Answer: A

Solution :

The imaginary surface joining the points of same potential in an electric field is called the equipotential surface,\[ie\], the potential difference between any two points on an equipotential surface is zero. Hence, if a charge is moved on an equipotential surface from one point to the other, no work is needed to be done. But this is possible only when the charge is moved perpendicular to the electric field (\[ie\], perpendicular to the lines of force). It means that the electric lines of force at each point of an equipotential surface are normal to the surface. Hence, the angle between electric field and equipotential surface is\[{{90}^{o}}\]. Alternative: Potential gradient along equipotential surface is zero. \[ie,\]    \[E\cos \theta =-\frac{dV}{dr}=0\] \[\therefore \]  \[\theta ={{90}^{o}}\]