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 of3 nC from infinity to the third corner of the triangle is __ $$\mu J$$
$$\frac{1}{4\pi \in_{\circ}}=9\times 10^{9}N.m^{2}/C^{2}$$

We need to find the work done in bringing a 3 nC charge from infinity to the third corner of an equilateral triangle.

q₁ = 1 nC, q₂ = 2 nC at two corners, side = 3 cm = 0.03 m, q₃ = 3 nC.

Work done = potential energy of q₃ due to q₁ and q₂:

$$W = q_3(V_1 + V_2) = q_3\left(\frac{kq_1}{r} + \frac{kq_2}{r}\right) = \frac{kq_3(q_1 + q_2)}{r}$$

$$W = \frac{9 \times 10^9 \times 3 \times 10^{-9} \times (1 + 2) \times 10^{-9}}{0.03}$$

$$= \frac{9 \times 10^9 \times 3 \times 10^{-9} \times 3 \times 10^{-9}}{0.03}$$

$$= \frac{81 \times 10^{-9}}{0.03} = 2700 \times 10^{-9} = 2.7 \times 10^{-6} \text{ J} = 2.7 \, \mu J$$

Therefore, the work done is Option 2: 2.7 μJ.