Q4. Assertion: the work done by an electrostatic field round any closed path is zero. Reason: the electrostatic force is conservative, so the work depends only on the end points. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: on a closed path the end points coincide (NCERT page 46).
Q5. Two positive charges are brought closer together slowly. Does their potential energy rise or fall? What if one is negative?
Like charges repel, so an external force must push them together: positive work, so the potential energy rises. Unlike charges attract; the external force must hold them back, doing negative work, so the potential energy falls (from NCERT Eq. (2.2), page 46).
Q6. A charge is carried from infinity to P, needing 8 × 10−6 J of external work, and then from P to Q, needing a further 2 × 10−6 J. Find UP and UQ, with U = 0 at infinity.
UP = 8 × 10−6 J and UQ = 8 × 10−6 + 2 × 10−6 = 1.0 × 10−5 J (NCERT Eqs. (2.2) and (2.3), pages 46–47).