Q4. Assertion: doubling the charge on a capacitor doubles the potential difference across it. Reason: the field between the conductors is proportional to the charge on them. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: V is the work per unit charge against that field, so V is proportional to Q and C = Q/V stays the same (NCERT page 67).
Q5. A capacitor stores 40 µC at 200 V. Find its capacitance and the charge it stores at 50 V.
C = Q/V = 40 × 10−6/200 = 0.20 µF. At 50 V, Q = CV = 0.20 × 10−6 × 50 = 10 µC (NCERT Eq. (2.38), page 67).
Q6. Find the capacitance of an isolated metal sphere of radius 9.0 cm, and the charge that raises it to 1000 V.
C = 4πε0R = 0.090/(9 × 109) = 1.0 × 10−11 F = 10 pF (see Example 2). Q = CV = 1.0 × 10−11 × 1000 = 1.0 × 10−8 C (NCERT Eq. (2.38), page 67).