Question

Magnetic field of magnitude $B_0$ exist in the region above the line as shown in figure. A charged particle of mass m and charge q moving at speed 'u' enters magnetic field region. Find time interval for which particle remains in magnetic field.

• A. $\frac{2\pi m\theta }{qB\pi }$
• B. $\frac{2\pi m}{qB}(1-\frac{\theta }{\pi })$
• C. $\frac{m\theta }{qB}$
• D. $\frac{2m\theta }{qB}(\frac{1}{\theta }-\frac{1}{\pi })$

Answer 1

The correct option is B $\frac{2\pi m}{qB}(1-\frac{\theta }{\pi })$

By geometry, $\alpha =2\theta$
Here, $T=\frac{2\pi R}{V}=\frac{2\pi m}{qB}$
So time $t=\frac{T}{2\pi }\times (2\pi -\alpha )$
$t=T(1-\frac{\alpha }{2\pi })=T(1-\frac{\theta }{\pi })$
$=\frac{2\pi m}{qB}(1-\frac{\theta }{\pi })$