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.
1/4πε₀=9× 10⁹ N· m²/C²

Solution

Physics sir · 4 steps

Work done on the 3 nC charge is its charge times the potential the other two create at that corner.

1. Work equals qV. Bringing a charge q slowly from infinity to a point needs work W = qV. Here V is the potential at that point due to the charges already there. Only the 1 nC and 2 nC charges count, and each sits 3 cm from the third corner.

   W = q 1/4πε₀ (q₁ + q₂)/r

2. Potential at the corner. Potential is a scalar, so the two contributions add directly, with no directions to worry about. With r = 0.03 m: V = (9 × 10⁹ × 3 × 10⁻⁹)/0.03 = 900 V.
3. Multiply by q. W = 3 × 10⁻⁹ × 900 = 2.7 × 10⁻⁶ J.
4. So. The work done is 2.7 μJ, which is option (c).

The idea to keep. Work to bring in one charge is qV at its final spot, using only the charges already present. The energy between the charges already placed is not part of this work.

Answer from the NTA final answer key. Solution by PrepWiser.