Q4. Assertion: the potential at every point on the equatorial plane of a dipole is zero. Reason: every such point is equally far from +q and −q. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: r = r, so q/r − q/r = 0 exactly, not only far away (NCERT Eq. (2.9), page 50).
Q5. A small dipole of moment 2 × 10−8 C m sits at the origin along +x. Find the potential at (0.3 m, 0) and at (−0.3 m, 0). Take k = 9 × 109 N m2 C−2.
kp/r2 = 9 × 109 × 2 × 10−8/0.09 = 2000 V. At (0.3 m, 0), on the +q side, V = +2000 V; at (−0.3 m, 0), V = −2000 V (NCERT Eq. (2.16), page 51).
Q6. Why is the potential of a small dipole axially symmetric about p?
Because it depends only on r and on the angle θ between r and p. Turning r round p keeps both, so P moves round a circle (the rim of a cone about p) on which the potential is the same (NCERT page 51).