Question:
Three point charges q, - 2q and - 2q are placed at the vertices of an equilateral triangle of side a. The work done by some external force to in crease their separation to 2a will be
Three point charges q, - 2q and - 2q are placed at the vertices of an equilateral triangle of side a. The work done by some external force to in crease their separation to 2a will be
Updated On: Jun 4, 2024
- $ \frac{ 1}{ 4 \pi \varepsilon_0 } \frac{ 2q^2 }{ a}$
- $ \frac{ 1}{ 4 \pi \varepsilon_0 } \frac{ q^2}{ 2a}$
- $ \frac{ 1}{ 4 \pi \varepsilon_0 } \frac{ 8 q}{ a^2 }$
- zero
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The Correct Option is D
Solution and Explanation
According to the question work done in increasing the
separation from a to 2a is
W = $ U_f - U_i$
Here, $ U_i = \frac{ 1}{ 4 \pi \varepsilon_0 } \bigg [ \frac{ q ( - 2q) }{ a} + \frac{ q ( - 2q) }{ a} + \frac{ ( - 2q) ( - 2q) }{ a} \bigg ] $
= $ \frac{ 1}{ 4 \pi \varepsilon_0 } [ - 2q^2 - 2q^2 + 4q^2 ] = 0 $
Similariy, $U_f$ is aiso zero
Hence, W = 0
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Concepts Used:
Electric Dipole
An electric dipole is a pair of equal and opposite point charges -q and q, separated by a distance of 2a. The direction from q to -q is said to be the direction in space.
p=q×2a
where,
p denotes the electric dipole moment, pointing from the negative charge to the positive charge.
Force Applied on Electric Dipole
