$A$ particle with charge $+Q$ and mass $m$ enters a magnetic field of magnitude $B,$ existing only to the right of the boundary $YZ.$ The direction of the motion of the particle is perpendicular to the direction of $B.$ Let $T = 2\pi\frac{m}{QB}.$ The time spent by the particle in the field will be:

• A
  $T\theta$
• B
  $2T\theta$
• C
  $T \left( \frac{\pi + 2\theta}{2\pi} \right)$
• D
  $T \left( \frac{\pi - 2\theta}{2\pi} \right)$