Question: Q. 5. For any charge configuration, equipotential surface through a point is normal to the electric field. Justify.
U [Delhi Set I, II, III 2014]
OR
Why must electrostatic field at the surface of a charged conductor be normal to the surface at every point? Give reason.
[Foreign 2014]
Show Answer
Solution:
Ans. If the electric field was not normal to the surface, then it would have a component along the surface which would cause work to be done in moving a charge on an equipotential surface.
$$ 1 $$
[CBSE Marking Scheme 2014]
Detailed Answer :
Equipotential lines are curved lines with similar altitude that pertains to electric potential or voltage. These lines are always perpendicular to electric field which create equipotential surfaces in three dimensions. The movement of charge along equipotential surface requires no work as movement is perpendicular to electric field. $1 / 2$ As work done in moving test charge along equipotential surface is zero, there appear fixed potential values across every point on equipotential surface, so where,
$$ W=F s \cos \theta=0 $$
$F=$ Electric force
$s=$ Magnitude of displacement of charge
In case of non-zero displacement, it exists only when
$$ \begin{aligned} & \cos \theta=0 \ & \Rightarrow \quad \theta=90^{\circ} \end{aligned} $$
Hence, force acting on point charge is perpendicular to equipotential surface.
