The potential at any point (x,y,z) in a space is given by $V = x^{2} y z$ . The work done in moving a charge 3C from point (1,2,3) to point (3,4,1) is .

30 J

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90 J

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36 J

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6 J

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Solution

The correct option is B 90 J
Work done in moving a charge from say point A to point B is given by $W = q (V_{B} - V_{A})$ where $V_{B} a n d V_{A}$ represent the potentials of point B and A respectively.
Here the particle is moved from A (1,2,3) to B (3,4,1)
$V_{B} = 3^{2} .4 .1 = 36 V$
and $V_{A} = 1^{2} .2 .3 = 6 V$
Work done = $q (V_{B} - V_{A}) = 3. (36 - 6) = 90 J$

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