Question

Explain the properties of an equiotential surface... There are two so explain both of them properly .

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Answer 1

$\huge{\underline{\underline{\mathfrak{Answer}}}}$

➡️Any surface over which the potential is constant is called an equipotential surface.In other words, the potential difference between any two points on an equipotential surface is zero.

Some important properties of equipotential surfaces :-

➡️Work done in moving a charge over an equipotential surface is zero.

➡️The electric field is always perpendicular to an equipotential surface.

➡️The spacing between equipotential surfaces enables us to identify regions of strong and weak fields.

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Answer 2

${ \blue{ \underline{ \mathcal{ \boxed{Equipotential \: Surface}}}}}$

•It is a surface in which the potential remains the same throughout . As the word itself implies "Equi" meaning Equal Potential.

${ \sf{ \underline{Properties}}} \: \implies$

→ Work done to move a test charge q through equipotential surface is Zero.

Proof : We know that

${ \sf{ \bold{V = \: \dfrac{ W}{Q }}}} \\ \\ \\ \implies \: V_a - V_b = \: \dfrac{ W}{Q }$

Now as it is an equipotential surface ,

${ \boxed{ \bold{V_a = V_b }}}$

•°• We get W/Q = 0

Hence Work done is Zero.

→ The electric field always acts at an angle of 90° to the surface.

Proof : As proved above , Work Done = 0

$W = F.dr \\ \\ \implies \: F \: dr \: \: cos \theta = 0$

[ Opening the dot product of two vectors ]

Now,

• F dr ≠ 0

$\implies \: cos \theta \: = 0 \\ \\ \ \: { \bold { \theta = 90 \degree}}$

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