A particle of charge q and mass m is projected with a velocity V 0 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 O P makes angle θ with the direction of V 0 , then the value of V 0 so that particle passes through O is -

Question

A particle of charge q and mass m is projected with a velocity V 0 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 O P makes angle θ with the direction of V 0 , then the value of V 0 so that particle passes through O is -, q B R m sin ⁡ θ, q B R 2 m sin ⁡ θ, 2 q B R m sin ⁡ θ, 3 q B R 2 m sin ⁡ θ

MARKS App · Accepted Answer

r = m V 0 q B R = 2 r sin ⁡ θ ⇒ R = 2 m V 0 q B sin ⁡ θ ⇒ V 0 = q B R 2 m sin ⁡ θ

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