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MOTION OF CHARGED PARTICLE IN UNIFORM MA...

MOTION OF CHARGED PARTICLE IN UNIFORM MAGNETIC FIELD WHEN V AND B ARE AT SOME ANGLE THAN 0, 90 AND 180

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What is the path followed by a charged particle when it moves at an angle (other than 0^@ , 90^@ or 180^@ ) to the magnetic field?

When a charged particle moving with velocity vec(V) is subjected to a magnetic field of induction vec(B) the force on it is non-zero. This implies that: (1.)angle between v and B is necessery 90 ∘ (2.)angle between v and B can have any value other than 90 ∘ (3.)angle between v and B can have any value other than zero and 180 ∘ (4.)angle between v and B is either zero or 180 ∘

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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