Three point charges, +Q, +2Q and -3Q are placed at the vertices of an equilateraltriangle ABC of side l. If these charges are displaced to the midpoints A1, B1 and C1respectively, find the amount of the work done in shifting the charges to the newlocations.

The work done in moving a charge in an electric field is given by the formula:

W = q * ΔV

where q is the charge and ΔV is the change in electric potential.

First, we need to calculate the initial potential at each vertex due to the other two charges. The potential V due to a point charge q at a distance r is given by:

V = k*q/r

where k is Coulomb's constant.

1. At vertex A, the potential due to the charges at B and C is:

   VA = k2Q/l + k(-3Q)/l = -k*Q/l

2. Similarly, at vertex B, the potential due to the charges at A and C is:

   VB = kQ/l + k(-3Q)/l = -2k*Q/l

3. And at vertex C, the potential due to the charges at A and B is:

   VC = kQ/l + k2Q/l = 3k*Q/l

Next, we calculate the potential at the midpoints due to the other two charges. The distance from each vertex to the midpoint of the opposite side in an equilateral triangle is l/2.

1. At midpoint A1, the potential due to the charges at B1 and C1 is:

   VA1 = k2Q/(l/2) + k(-3Q)/(l/2) = -2k*Q/l

2. Similarly, at midpoint B1, the potential due to the charges at A1 and C1 is:

   VB1 = kQ/(l/2) + k(-3Q)/(l/2) = -4k*Q/l

3. And at midpoint C1, the potential due to the charges at A1 and B1 is:

   VC1 = kQ/(l/2) + k2Q/(l/2) = 6k*Q/l

Finally, we calculate the work done in moving each charge from its initial position to its final position:

W = Q*(VA1 - VA) + 2Q*(VB1 - VB) + (-3Q)*(VC1 - VC)

Substituting the values we calculated above:

W = Q*(-2kQ/l - (-kQ/l)) + 2Q*(-4kQ/l - (-2kQ/l)) + (-3Q)(6kQ/l - 3k*Q/l)

Simplifying:

W = -kQ^2/l + 4kQ^2/l + 9kQ^2/l = 12kQ^2/l

So the work done in shifting the charges to the new locations is 12k*Q^2/l.