An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area 24   cm 2 . The two ends of the wire are connected to a resistor. The total resistance in the circuit is 12   Ω . If an externally applied uniform magnetic field in the core along its axis changes from 1 . 5   T in one direction to 1 . 5   T in the opposite direction, the charge flowi

Step-by-step solution

The induced emf ε in the turns of the coil can be written as ε = - d φ d t = i R       . . . 1 Simplify equation (1) to obtain the required charge through a point in the circuit. - d φ d t = i R ⇒ - 1 R ∫ φ 1 φ 2 d φ = ∫ i d t ⇒ q = φ 1 - φ 2 R       . . . 2 Where, φ 1 ,   φ 2 are the magnetic flux associated with the coil from two ends. As, φ = N B A , from equation (2), it can be written that q =