Question

Statement 1: For a charged particle moving from point P to point Q, the net work done by an electrostatic field on the particle is independent of the path connected point P to point Q.
Statement 2: The net work done by conservative force on an object moving along a closed loop is zero.
(A) Statement 1 is True, Statement 2 is False.
(B) Statement 1 is True, Statement 2 is True; Statement 2 is a correct explanation for Statement 1.
(C) Statement 1 is True, Statement 2 is True; Statement 2 is not a correct explanation for Statement 1.
(D) Statement 1 is False, Statement 2 is True.

Answer 1

The particle moving in an electrostatic force is under a conservative force. So the work done by the particle will be path independent of path. And for any conservative force, the total work done in a closed loop will be zero.

Complete step by step solution:
When a particle is under a conservative force, and it moves from one position to another, then the value of the work done only depends on the initial and the final position of the particle. The path taken by the particle to reach the final point from the initial point does not affect the work done.
So in the case of a closed loop, the initial and the final position of the particle is the same. So the work done by the particle will only depend on the initial and final position, which is the same in this case, and as the particle is under the effect of a conservative force, so the work done by the particle will be zero in a closed loop.
Hence the second statement is true.
In the first statement, the particle is said to be moving in the presence of an electrostatic field. Now the magnitude of the electrostatic field is constant at every point. Therefore the force on every point on the particle is constant. Therefore, this is a conservative force and hence, the work done on the particle will be independent of the path that will be followed by the particle.
So statement 1 is also true and statement 2 is not a correct explanation of statement 1.
Therefore option (C) is correct.

Note:
A conservative force is that which has a property that the force acting on the particle will be independent of the path that is followed by the particle. Some examples of conservative forces are, electrostatic force, magnetic force, force in an elastic spring, etc.