JEE Advanced2021PhysicsElectromagnetic InductionActual
A long straight wire carries a current, I = 2 ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at distances 1 cm and 4 cm from the wire. At time t = 0 , the rod starts moving on the
Options
- AMaximum current through R is 1.2 × 10 − 6 ampere
- BMaximum current through R is 3.8 × 10 − 6 ampere.
- CMaximum charge on capacitor C 0 is 8.4 × 10 − 12 coulomb.
- DMaximum charge on capacitor C 0 is 2 .4 × 10 − 12 coulomb.
Correct answer
A. Maximum current through R is 1.2 × 10 − 6 ampere
Step-by-step solution
Magnetic field due the long wire, B = μ 0 I 2 π x Motional emf in small element, d ε = B v d x = 3 μ 0 2 2 π x d x ⇒ ε = 3 μ 0 π ∫ 1 4 1 x d x ∴     ε = 3 μ 0 π ln 4 = 16.8 × 10 − 7 Maximum charge on capacitor, q max = ε C = 16.8 × 10 − 7 5 × 10 − 6 = 84 × 10 − 13   C = 8.4 × 10 − 12   C Maximum current in circuit, I max = ε R = 16.8 × 10 − 7 1.4 =