Q4. Assertion: the potential energy of a system of charges does not depend on the order in which the charges are brought in. Reason: the work done by the electrostatic force does not depend on the path. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion (NCERT page 56).
Q5. Charges +q, +q and −2q sit at the corners of an equilateral triangle of side a. Find the potential energy of the system.
U = k[q·q + q(−2q) + q(−2q)]/a = k(q2 − 4q2)/a = −3kq2/a (NCERT Eq. (2.26), page 56).
Q6. Four equal charges q sit at the corners of a square of side d. Find the potential energy.
Four sides give 4kq2/d and two diagonals give 2kq2/(√2 d) = √2 kq2/d, so U = (4 + √2)kq2/d (as in NCERT Example 2.4, pages 57–58).
Q7. Two small identical spheres, each with +1.0 µC, are held 10 cm apart and released. What is their total kinetic energy when they are far apart?
U = kq2/r = 9.0 × 10−3/0.10 = 0.090 J. As they fly apart, U falls to zero and becomes kinetic energy: 0.090 J in all, 0.045 J each (reasoned from NCERT Eq. (2.22), page 56, and conservation of energy).