Q4. Assertion: the surface charge density of a conductor is a macroscopic quantity. Reason: it is averaged over area elements that are small on the everyday scale but contain very many charges. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion (NCERT page 28).
Q5. A wire bent into a circle of radius 0.1 m carries a linear charge density of 5 × 10−9 C/m. Find its total charge.
Q = λ × 2πR = (5 × 10−9)(2π × 0.1) ≈ 3.1 × 10−9 C (NCERT Eq. (1.24), page 28).
Q6. A thin ring of radius R carries positive charge Q spread uniformly. Consider distances x ≥ 0 along one side of its axis. (a) Find the field on its axis at x = R. (b) At what distance along the axis is the field largest?
(a) At x = R, x2 + R2 = 2R2, so E = kQR/(2R2)3/2 = kQ/(2√2 R2). (b) E is zero at the centre and falls off like a point charge’s far away, so it has a maximum. Setting dE/dx = 0 gives x2 + R2 = 3x2, so x = R/√2, where E = 2kQ/(3√3 R2) ≈ 0.38kQ/R2. Every positive field value smaller than the maximum, including the one in (a), occurs at two finite distances, one on each side of R/√2. (From Example 4.)