Q4. Assertion: the forces that two long parallel wires exert on each other are equal and opposite even when their currents differ. Reason: each force is proportional to the product IaIb. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: the force on each wire is μIaIbL/(2πd), the same product for both, and the directions are opposite, Fba = −Fab (NCERT Eqs. (4.17)–(4.18), page 123).
Q5. Three long parallel wires lie in one plane, 10 cm apart, each carrying 5.0 A in the same direction. Find the force per metre on the middle wire and on an outer wire.
Middle wire: pulled equally both ways, so zero. Outer wire: f = 2 × 10−7 × 25/0.10 + 2 × 10−7 × 25/0.20 = 5.0 × 10−5 + 2.5 × 10−5 = 7.5 × 10−5 N/m, towards the middle (NCERT Eq. (4.19), page 123).
Q6. A long straight wire carries 10 A. A rectangular loop, 10 cm by 5.0 cm, lies in the same plane with its 10 cm sides parallel to the wire, the nearer one 2.0 cm away, and carries 5.0 A, flowing the same way as the wire’s current in the nearer side. Find the net force on the loop.
The nearer side is attracted and the farther side, with the opposite current, is repelled; the forces on the two short sides cancel. Net force = 2 × 10−7 × 10 × 5.0 × 0.10 × (1/0.020 − 1/0.070) ≈ 3.6 × 10−5 N, towards the wire (reasoned from NCERT Eq. (4.17), page 123).
Q7. Use NCERT Eq. (4.19) to find the SI unit of μ.
From NCERT Eq. (4.19), μ = 2πdf/(IaIb), so its unit is m × (N/m)/A = N A−2, the same as T m A−1.