Question

charges 2 micro coulomb, 4 micro coulomb and 6 micro coulomb are placed at the three corners A, B and C respectively of a square ABCD of side X meter. find what charge must be placed at the fourth corner so that the total potential at the centre of the square is zero​

Answer 1

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Answer 2

Answer:

The charge that must be placed at corner D of the square so that the total potential at the center of the square is zero is -12 micro-coulombs.

Explanation:

To find the charge that must be placed at the fourth corner so that the total potential at the center of the square is zero, we need to use the concept of electric potential due to point charges.

Let's consider a point P at the center of the square ABCD. The electric potential V at point P due to a point charge q at a distance r is given by:

V = kq/r

where k is the Coulomb's constant.

Using the principle of superposition, we can find the total electric potential at point P due to the three charges placed at the corners A, B, and C of the square. Let's assume that the fourth charge q4 is placed at corner D. Then the distances between the charges and the point P are as follows:

Distance from A to P = (X/2) * √2

Distance from B to P = (X/2) * √2

Distance from C to P = (X/2) * √2

Distance from D to P = X/2

So the total electric potential V at point P due to the three charges at A, B, and C is:

V = kq1/(X/2 * √2) + kq2/(X/2 * √2) + kq3/(X/2 * √2)

V = k(X/2 * √2) * (q1 + q2 + q3)/X

V = k√2(q1 + q2 + q3)

We want the total electric potential V to be zero at point P. So we can write:

k√2(q1 + q2 + q3 + q4) = 0

q1 + q2 + q3 + q4 = 0

Substituting the values of q1, q2, and q3, we get:

2μC + 4μC + 6μC + q4 = 0

q4 = -2μC - 4μC - 6μC

q4 = -12μC

Therefore, the charge that must be placed at corner D of the square so that the total potential at the center of the square is zero is -12 micro-coulombs.

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