In the xy - plane , the region y > 0 has a uniform magnetic field B...

Average speed along the (\mathrm{x})-axis (\left(\mathrm{V}_{\mathrm{x}}\right)=\frac{\int\left|\overrightarrow{\mathrm{V}_{\mathrm{x}}\right| \mathrm{dt}}{\int \mathrm{dt}}=\frac{\mathrm{d}_1+\mathrm{d}_2}{\mathrm{t}_1+\mathrm{t}_2} \rightarrow(1)) We also have, $$\begin{aligned} &\mathrm{r}_1=\frac{\mathrm{mv}}{\mathrm{qB}_1}, \mathrm{r}_2=\frac{\mathrm{mv}}{\mathrm{qB} \mathrm{B}_2} \\ &\text{ since } \mathrm{B}_1=\frac{\mathrm{B}_2}{4} \end{aligned}$$) (\therefore \mathrm{r}_1=4 \mathrm{r}_2 \rightarrow(2)) Time$in$(B_1 \Rightarrow \frac{\pi B}{q B_1}=t_1) Time in (\mathrm{B}_2 \Rightarrow \frac{\pi \mathrm{B}}{\mathrm{qB}_2}=\mathrm{t}_2) Total distance along (\mathrm{x})-axis (\mathrm{d}_1+\mathrm{d}_2=2 \mathrm{r}_1+2 \mathrm{r}_2=2\left(\mathrm{r}_1+\mathrm{r}_2\right)=2\left(5 \mathrm{r}_2\right)) Total time ($\mathrm{T}=\mathrm{t}$_1+\mathrm{t}_2=5 \mathrm{t}_2) (\therefore \text{ Average speed }=\frac{10 \mathrm{r}_2}{5 \mathrm{t}_2}=2 \frac{\mathrm{mv}}{\mathrm{qB}_2} \times \frac{\mathrm{qB}_2}{\pi \mathrm{m}}=2)$