Question

Two charges moving under their only own mutual attraction separated by large distance initially. Then choose the correct statement (s):

• A. If both are free, mechanical energy is conserved.
• B. If one is fixed and other is free, mechanical energy is conserved.
• C. If one is fixed and other is free, momentum is conserved.
• D. If both are free momentum is conserved.

Answer 1

Answer: (A), (B), (D)

Options 1, 2, and 4 are correct.

Answer 2

Solution

1. Both free: No external forces act so the mutual (conservative) force conserves mechanical energy and also the system’s total momentum is conserved.

2. One fixed, one free: The free particle moves in a conservative potential provided by the fixed charge. Even though the fixed charge is held in place (by an ideal constraint doing no work), the energy (kinetic + potential) of the free charge is conserved. However, because of the external constraint, momentum of the free charge alone (or the system defined this way) is not conserved.

Thus, correct statements are:

• If both are free, mechanical energy is conserved.
• If one is fixed and the other is free, mechanical energy is conserved.
• If both are free, momentum is conserved.

Core Explanation:

For two free charges, no external forces implies both energy and momentum conservation. When one charge is fixed (by an ideal constraint that does no work), the free charge’s energy (kinetic + potential) remains conserved, but momentum is not conserved due to the external fixing force.