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 $$12 \ \Omega$$. 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 flowing through a point in the circuit during the change of magnetic field will be _____ mC.

The charge flowing through the circuit when magnetic field changes:

$$q = \frac{N \Delta \Phi}{R} = \frac{N \times \Delta B \times A}{R}$$

The magnetic field changes from 1.5 T to -1.5 T (opposite direction), so:

$$\Delta B = 1.5 - (-1.5) = 3 \text{ T}$$

Given: $$N = 100$$, $$A = 24 \text{ cm}^2 = 24 \times 10^{-4} \text{ m}^2$$, $$R = 12 \text{ }\Omega$$.

$$q = \frac{100 \times 3 \times 24 \times 10^{-4}}{12} = \frac{0.72}{12} = 0.06 \text{ C} = 60 \text{ mC}$$

The charge flowing is $$\mathbf{60}$$ mC.