CBSE Class 12 Physics 2014 Delhi Set 1 Paper

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Question : 3
Total: 30
For any charge configuration, equipotential surface through a point is normal to the electric field. Justify.
Solution:  
A surface where the potential is constant is referred to as an equipotential surface. That indicates that there is no work is involved in moving a charge along an equipotential surface from one point to another. In an equipotential surface, the potential difference between any two points is also zero.

That is, the Work done can be given as,
W=Fscosθ=0
Here, F is the electric force and s is the magnitude of displacement
Now we know that, for a non-zero displacement, the cosθ should be equal to zero
That is, cosθ=0
Or θ=90
This explains that the force acting on a point charge on an equipotential surface is vertical.

It is well known that the electric field lines indicate the direction of the electric force acting on a charge.
Therefore, we may say that the equipotential surface via a point is normal to the electric field for any charge arrangement.
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