our identical charges +50 μC each are placed, one at each corner of a square of side 2m. How much external energy is required to bring another charge of +50 μC from infinity to the centre of the square

To solve this problem, we need to calculate the potential energy at the center of the square due to the four charges at the corners.

Step 1: Calculate the distance from the center of the square to one of the corners.

Since the square has a side length of 2m, the diagonal of the square is √2 * side = √2 * 2m = 2.83m. The distance from the center of the square to one of the corners is half of the diagonal, which is 2.83m/2 = 1.41m.

Step 2: Calculate the potential energy due to one charge.

The formula for potential energy due to a point charge is U = kq1q2/r, where k is Coulomb's constant (910^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between them.

Here, q1 = q2 = +50 μC = 5010^-6 C, r = 1.41m, so U = 910^9 * 5010^-6 * 5010^-6 / 1.41 = 0.014 Joules.

Step 3: Multiply the potential energy by 4.

Since there are four charges at the corners of the square, the total potential energy at the center of the square is 4 * U = 4 * 0.014 Joules = 0.056 Joules.

Step 4: Calculate the external energy required to bring another charge of +50 μC from infinity to the center of the square.

The external energy required is equal to the potential energy at the center of the square, which is 0.056 Joules.