Question

The region between $x=0$ and $x=L$ is filled with uniform, steady magnetic field $B_0\hat{k}$. A particle of mass m, positive charge q and velocity $v_0\hat{i}$ travels along x-axis and enters the region of magnetic field. Neglect gravity throughout the question. The field now extends up to $x=2.1L$ If the time spent by the particle in the magnetic field is $T=\frac{\pi m}{X\times q{B}_0}$. Find X?

Answer 1

In this case, $x=\frac{2.1m{v}_0}{2q{B}_0}>r$
Hence, the particle will complete semicircular path and emerge from the field with velocity $-v_0\hat{i}$ as shown in fig.

Time spent by the particle in the magnetic field:
$T=\frac{\pi r}{v_0}=\frac{\pi m}{q{B}_0}$
The speed of the particle does not change due to magnetic field.