Question

Q/C S Starting with the definition of work, prove that at every point on an equipotential surface, the surface must be perpendicular to the electric field there.

Answer 1

It is proved that at every point on an equipotential surface, the surface must be perpendicular to the electric field.

What is meant by equipotential surface?

• An equipotential surface is any surface where the potential is constant. In other words, any two points on an equipotential surface have the same potential difference.
• Equipotential surfaces have the following important properties: 1. The work done in moving a charge across an equipotential surface is equal to zero.
• An equipotential surface is one on which all of the points on it have the same electric potential.
• This means that a charge has the same potential energy at all points along the equipotential surface.

• We have to prove that at every point on an equipotential surface, the surface must be perpendicular to the electric field.

The potential between two points (A) and (B) on an equipotential surface is given by:

W AB = q ΔV = -q $\int\limits^A_B$ E dS

By the definition  ΔV at an equipotential surface is zero.

-q $\int\limits^A_B$ E dS = 0

$\int\limits^A_B$ E dS = 0

$\int\limits^A_B$ ES cos θ = 0

Therefore, cos θ must be 0° or 90° for a field to be non electric.

Hence, it is proved that at every point on an equipotential surface, the surface must be perpendicular to the electric field.

To learn more about equipotential surfaces, refer to:

brainly.com/question/14675095

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