BITSAT 2024 Shift 1 Paper

The changing magnetic field induces an electric field, which accelerates the electron.To determine the acceleration of the electron, we use the formula:$a = \frac{eE}{m}$where $F = qE$.To calculate the electric field $E$, we apply Faraday's law of electromagnetic induction:$\varepsilon = -\frac{d\Phi}{dt} = -B \cdot A$Here, $B$ is the magnetic field, and $A$ is the cross-sectional area. Therefore, the electromotive force (emf) is:$\varepsilon = -A \cdot \frac{dB}{dt} = -\pi r^2 \cdot \frac{dB}{dt}$The electric field $E$ is then given by:$E = -\frac{\varepsilon}{\text{distance}} = -\frac{\varepsilon}{d}$$E = \frac{\pi r^2}{d} \cdot \frac{dB}{dt}$Finally, the acceleration $a$ is:$a = \frac{e}{m} \cdot \frac{\pi r^2}{d} \cdot \frac{dB}{dt}$Substituting the given values:$a = \frac{1.6 \times 10^{-19}}{9.1 \times 10^{-31}} \times \frac{22}{7} \times \frac{(0.5)^2}{0.3} \times 50 \times 10^{-6}$$= 23 \times 10^6 \mathrm{ms}^{-2}$