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Three point charges +Q, +2Q and -3Q are ...

Three point charges `+Q, +2Q and -3Q` are placed at the vertices of an equilateral triangle ABC of side l. If these charges are displaced at the find points `A_(1), B_(1) and C_(1)` respectively, find the amount of work done in shifting the charges to their new positions.

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To find the amount of work done in shifting the charges \( +Q, +2Q, \) and \( -3Q \) from points \( A, B, C \) to new positions \( A_1, B_1, C_1 \) respectively, we need to calculate the initial and final potential energies of the system and then determine the work done based on the change in potential energy. ### Step 1: Calculate the Initial Potential Energy The initial potential energy \( U_i \) of the system can be calculated using the formula for the potential energy between point charges: \[ U_i = k \sum_{i
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