Electrostatics

JEE Main level, single correct, medium

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Question 151 of 311

Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm. The work done in bringing a charge of 3 nC from infinity to the third corner of the triangle is ____\_\_\_\_ μJ\mu \mathrm{J}.
14πϵ0=9×109 N.m2/C2\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \mathrm{~N}. \mathrm{m}^{2} / \mathrm{C}^{2}

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Answer: (C) 2.7

Two point charges of 1 nC and 2 nC are placed at two corners of an equilateral triangle with side 3 cm. The work done in bringing a 3 nC charge from infinity to the third corner equals the charge times the potential at that point.
Both source charges are at distance 0.03 m from the third corner.
The potential due to the 1 nC charge is V1=9×109×1×10−90.03=300V_1 = \frac{9 \times 10^9 \times 1 \times 10^{-9}}{0.03} = 300 V
and due to the 2 nC charge is V2=9×109×2×10−90.03=600V_2 = \frac{9 \times 10^9 \times 2 \times 10^{-9}}{0.03} = 600 V.
Total potential: Vtotal=300+600=900V_{total} = 300 + 600 = 900 V
Work done: W=3×10−9×900=2.7×10−6W = 3 \times 10^{-9} \times 900 = 2.7 \times 10^{-6} J = 2.7 μJ

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