Inside a solenoid of radius 0.5 m , magnetic field is changing at a...

The changing magnetic field induce an electric field which will accelerate the electron. The acceleration of electron will be $a=\frac{e E}{m} \quad[\because F=q E]$ To find electric field $E$, we will use Faraday's electromagnetic induction. $\mathrm{emf}, \varepsilon=\frac{-d \phi}{d t}(B \cdot A)$ where, $B$ is the magnetic field and $A$ is the area of cross-section. $\varepsilon=-A \cdot \frac{d B}{d t}=-\pi r^2 \frac{d B}{d t}$ Now, electric field, $E=-\frac{\mathrm{emf}}{\text{ distance }}=-\frac{\dot{\varepsilon}}{d}=\frac{\pi r^2}{d} \frac{d B}{d t}$ Now, acceleration, $a=\frac{e}{m} \frac{\pi r^2}{d} \frac{d B}{d t}=\frac{1.6 \times 10^{-19}}{9.1 \times 10^{-31}} \times \frac{22}{7}$$\begin{aligned} & \times \frac{(0.5)^2}{(0.3)} \times 50 \times 10^{-6} \\ & =23 \times 10^6 \mathrm{ ms}^{-2}\end{aligned}$$$