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When a particle of charge $10 μC$ is brought from infinity to a point in the electric field, $10 mJ$ work is done by the external forces. The potential at that point is

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1000 V

1500 V

1050 V

None of the above

answer is A.

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Detailed Solution

When a particle of charge

10 μC

is brought from infinity to a point in the electric field,

10 mJ

work is done by the external forces and the potential at that point is

1000 J

.
It is given that

W = 10 mJ

\Rightarrow W = 10 \times 1 0^{- 3} J

\Rightarrow W

= 10^{- 2} J

Therefore

10^{- 2} J

of work is done to bring

Q = 10 μC

of charge from infinity to any point.

Q = 10 \times 10^{- 6} C

\Rightarrow Q = 10^{- 5} C

“The potential

(V)

at any point can be defined as the work done

(W)

in bringing a unit positive charge

(Q)

from infinity to any point.” Mathematically, the potential at a point can be written as

V = \frac{W}{Q}

On substituting the given values, we get the potential as

\Rightarrow V = \frac{10^{- 2}}{10^{- 5}}

\Rightarrow V = 10^{+ 3}

\Rightarrow V = 1000 V

Hence, the potential is equal to

1000 V

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