(D) When a charged particle enters a perpendicular magnetic field,it follows a circular path. The time period of a full circular orbit is $T = \frac{2

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$T \left( \frac{\pi - 2\theta}{2\pi} \right)$

(D) When a charged particle enters a perpendicular magnetic field,it follows a circular path. The time period of a full circular orbit is $T = \frac{2\pi m}{QB}$.From the geometry of the path,the particle enters the field at an angle $\theta$ with the normal to the boundary $YZ$. The angle subtended by the arc of the circular path inside the magnetic field at the center is $\phi = \pi - 2\theta$.The time spent in the magnetic field is given by $t = \frac{\phi}{2\pi} T$.Substituting $\phi = \pi - 2\theta$,we get $t = \frac{\pi - 2\theta}{2\pi} T = T \left( \frac{\pi - 2\theta}{2\pi} \right)$.

Class 12 Physics Moving Charges and Magnetism Motion of Charged Particle In Magnetic Field

$A$ 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
$T \left( \frac{\pi - 2\theta}{2\pi} \right)$

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Moving Charges and Magnetism

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Motion of Charged Particle In Magnetic Field

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