Two charges of 2mC and 8mC are kept at 2m,7m respectively .At what position third charge be placed so that all are in equilibrium . calculate magnitude of charge?

Question

Answer

Explanation:

Given:
- Charge 1 (q1) = 2mC, positioned at (2m, 0m)
- Charge 2 (q2) = 8mC, positioned at (0m, 7m)
- Charge 3 (q3) = ?, positioned at (x, y)

Equilibrium Condition:
For the charges to be in equilibrium, the net force acting on the third charge should be zero. This means that the net electrostatic force due to charges 1 and 2 on charge 3 should cancel out.

Calculating the Distance and Charge:
- The distance between charge 1 and charge 3 is given by: d1 = √[(x-2)^2 + y^2]
- The distance between charge 2 and charge 3 is given by: d2 = √[x^2 + (y-7)^2]

Applying the Equilibrium Condition:
- The force due to charge 1 on charge 3 is given by: F1 = k * q1 * q3 / d1^2
- The force due to charge 2 on charge 3 is given by: F2 = k * q2 * q3 / d2^2

Since the charges are in equilibrium, F1 and F2 should be equal in magnitude but opposite in direction.

Solving for the Unknown Charge:
- Set F1 = F2 and solve for q3 to find the magnitude of the charge that needs to be placed at position (x, y) to maintain equilibrium.

By solving the equations for charge 3, you can determine the magnitude required to maintain equilibrium between the three charges positioned at their respective locations.

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