Three particles,each having a charge of 10microC,are placed at the vertices of an equilateral triangle of side 10cm .find the work done by a person in pulling them apart to infinite separations?

Question

Answer

The answer should be the change in potential energy of the system of particles. As at infinity the potential energy of the system will be zero so the initial potential energy, which is the sum of potential energy of each pair will be the required change and hence the work done.

Answer

Work done in separating the charges to infinite separation:
- First, calculate the potential energy of the system when the charges are at the vertices of the equilateral triangle:
- The potential energy of a system of charges is given by the formula U = k * (q1 * q2) / r, where k is the electrostatic constant, q1 and q2 are the charges, and r is the separation between the charges.
- In this case, the potential energy of the system when the charges are at the vertices of the equilateral triangle is U = 3 * k * (10 * 10 * 10^-6) / 10 cm.
- Next, calculate the work done by a person in pulling the charges apart to infinite separation:
- As the charges are pulled apart, the potential energy of the system increases to zero when the charges are separated to infinite distance.
- The work done in pulling the charges apart to infinite separation is equal to the change in potential energy of the system, which is the initial potential energy of the system when the charges are at the vertices of the equilateral triangle.
- Therefore, the work done by a person in pulling the charges apart to infinite separation is equal to the initial potential energy of the system.
- Substituting the values, we get:
- U = 3 * k * (10 * 10 * 10^-6) / 10 cm = 3 * (9 * 10^9) * (10 * 10^-6) / 0.1 = 2.7 J.
- Hence, the work done by a person in pulling the charges apart to infinite separation is 2.7 Joules.

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