Q4. Assertion: the work done in bringing a charge from infinity to a point near a point charge does not depend on the path. Reason: any small step can be split into a part along the radius and a part across it, and the part across it needs no work. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion (NCERT Example 2.1, page 49).
Q5. Two points are 0.1 m and 0.4 m from a 2.0 nC charge. Find the potential difference between them. Take k = 9 × 109 N m2 C−2.
kQ = 18 V m, so V = 180 V at 0.1 m and 45 V at 0.4 m: the nearer point is 135 V higher (NCERT Eq. (2.8), page 48).
Q6. An α-particle (charge +2e) is brought from far away to 1.0 × 10−13 m from a gold nucleus (charge +79e). How much work is needed, in MeV?
V = k(79e)/r = 9 × 109 × 79 × 1.6 × 10−19/10−13 ≈ 1.14 × 106 V, so W = qV = 2e × 1.14 × 106 V ≈ 2.3 MeV (NCERT Eq. (2.8), page 48; 1 MeV = 1.6 × 10−13 J, page 59).