Question

The magnetic field shown in the figure consist of the two magnetic fields.
If V is the velocity just required for a charge particle of mass $m$ and charge $-q$ to pass through the magnetic field. Particle is projected with velocity V perpendicular to the fields, then how much time does the charge spend in the magnetic field (W represent the radius of circular path traced by charge)

• A. $\frac{\pi m}{2qB}$
• B. $\frac{\pi m}{qB}$
• C. $\frac{\pi m}{4qB}$
• D. $\frac{3\pi m}{2qB}$

Answer 1

The correct option is B $\frac{\pi m}{qB}$

Angular speed is independent of speed. Particle will travel as shown.
Time = $\frac{2\pi m}{qB}\times \frac{1}{4}+\frac{2\pi m}{q\left(2B\right)}\times \frac{1}{2}=\frac{\pi m}{2qB}+\frac{\pi m}{2qB}=\frac{\pi m}{qB}$