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Question: A particle of charge q and mass m is projected with a velocity V<sub>0</sub> towards a circular regi...

A particle of charge q and mass m is projected with a velocity V0 towards a circular region having uniform magnetic field B perpendicular and into the plane of paper from point P as shown in the figure. R is the radius and O is the centre of the circular region. If the line OP makes angle q with the direction of V0, then the value of V0 so that particle passes through O is–

A

B

C

2qBRmsin⁡θ\frac { 2 q B R } { m \sin \theta }

D

Answer

Explanation

Solution

r = mV0qB\frac { \mathrm { mV } _ { 0 } } { \mathrm { qB } }

R = 2 r sin q

Ž R = sin q

Ž V0 = qBR2 msin⁡θ\frac { \mathrm { qBR } } { 2 \mathrm {~m} \sin \theta }