Q4. Assertion: the potential energy of a dipole in a uniform field is least when the dipole points along the field. Reason: U = −pE cos θ is −pE at θ = 0. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion (NCERT Eq. (2.32), page 60).
Q5. Two charges of +1 µC each sit 0.30 m apart, at points where an external potential is 200 V and 500 V. Find the potential energy of the system.
qV terms: 10−6 × 200 + 10−6 × 500 = 7.0 × 10−4 J. Mutual term: 9 × 109 × 10−12/0.30 = 3.0 × 10−2 J. Total ≈ 3.07 × 10−2 J (NCERT Eq. (2.29), page 59).
Q6. A dipole’s energy is −4 mJ when it lies along a uniform field. What is it at 60° to the field, and how much work turns it from 0° to 60°?
pE = 4 mJ, so U(60°) = −4 cos 60° = −2 mJ, and the work is pE(cos 0° − cos 60°) = 2 mJ (NCERT Eqs. (2.31)–(2.32), page 60).