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A charged particle moves in a uniform ma...

A charged particle moves in a uniform magnetic field. The velocity of the particle at some instant makes an acute angle with the magnetic field. The path of the particle will be

A

A straight line

B

A circle

C

A helix with uniform pitch

D

A helix with non-uniform pitch

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The correct Answer is:
C
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The path of a charged particle in a uniform magnetic field depends on the angle theta between velocity vector and magnetic field, When theta is 0^(@) or 180^(@), F_(m) = 0 hence path of a charged particle will be linear. When theta = 90^(@) , the magnetic force is perpendicular to velocity at every instant. Hence path is a circle of radius r = (mv)/(qB) . The time period for circular path will be T = (2pim)/(qB) When theta is other than 0^(@), 180^(@) and 90^(@) , velocity can be resolved into two components, one along vec(B) and perpendicular to B. v_(|/|)=cos theta v_(^)= v sin theta The v_(_|_) component gives circular path and v_(|/|) givestraingt line path. The resultant path is a helical path. The radius of helical path r=(mv sin theta)/(qB) ich of helix is defined as P=v_(|/|)T P=(2 i mv cos theta) p=(2 pi mv cos theta)/(qB) A charged particle moves in a uniform magnetic field. The velocity of particle at some instant makes acute angle with magnetic field. The path of the particle will be

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