Q4. Assertion: a dipole in a uniform electric field can rotate but its centre of mass has no electric acceleration. Reason: the forces on its two charges are equal and opposite but act at different points. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: the forces cancel, giving zero net force, but form a couple that gives a torque (NCERT page 27).
Q5. A dipole feels a torque of 4 × 10−5 N m when it is at 30° to a field of 2 × 103 N C−1. Find its dipole moment.
p = τ/(E sin θ) = (4 × 10−5)/(2 × 103 × 0.5) = 4 × 10−8 C m (NCERT Eq. (1.22), page 27).
Q6. A small dipole is placed antiparallel to a field whose direction is the same at both ends and whose strength has a nonzero gradient along the dipole. Is there a torque? Is there a net force, and which way?
No torque, since p and E are antiparallel. There is a net force, in the direction of decreasing field (NCERT page 27).
Q7. A dipole of moment p and moment of inertia I is released at a small angle to a uniform field E. How does it move?
It oscillates about θ = 0. For small θ, τ = −pE sin θ ≈ −pEθ, the condition for simple harmonic motion, so
(reasoned from τ = pE sin θ, NCERT Eq. (1.22), page 27; the period is not in NCERT’s text).