Physics Question from JEE Main 2023 · 13 April, Shift 2

An insulated copper wire of $100$ turns is wrapped around a wooden cylindrical core of cross-sectional area $24 \, \text{cm}^2$. The two ends of the wire are connected to a resistor and the total resistance in the circuit is $12 \, \Omega$. If an externally applied uniform magnetic field in the core along its axis changes from $1.5 \, \text{T}$ in one direction to $1.5 \, \text{T}$ in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be _____ $\text{mC}$.