A point charge of is placed at the origin. The work done in moving a point charge from point is ______J. [2026]

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Solution

Q.
A point charge of $10^{- 8} C$ is placed at the origin. The work done in moving a point charge $2 μ C$ from point $A (4, 4, 2) to B (2, 2, 1)$ is ______J. $(\frac{1}{4 π ε_{0}} = 9 \times 10^{9} in SI units)$ [2026]

1 0

2 $15 \times 10^{- 6}$

3 $30 \times 10^{- 6}$

4 $45 \times 10^{- 6}$

Ans.
(3)

Work done by external agent :

$W_{ext} = Δ U;$

$Δ U \to Change in potential energy in taking the charge from initial to final configuration$

$\Rightarrow W_{ext} = \frac{1}{4 π ε_{0}} \frac{q_{1} q_{2}}{r_{f}} - \frac{1}{4 π ε_{0}} \frac{q_{1} q_{2}}{r_{i}}$

$Now, r_{f} = \sqrt{{(2 - 0)}^{2} + {(2 - 0)}^{2} + {(1 - 0)}^{2}} = 3 m$

$r_{i} = \sqrt{{(4 - 0)}^{2} + {(4 - 0)}^{2} + {(2 - 0)}^{2}} = 6 m$

$∴$ $W_{ext} = (9 \times 10^{9}) \times (10^{- 8} \times 2 \times 10^{- 6}) [\frac{1}{3} - \frac{1}{6}]$

$= 3 \times 10^{- 5}$

$= 30 \times 10^{- 6} J$

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