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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)` Two ions having masses in the ratio 1:1 and charges 1:2 are projected from same point into a uniform magnetic field with speed in the ratio 2:3 perpendicular to field. The ratio of radii of circle along which the two particles move is :A. `4:3`B. `2:3`C. `3:2`D. `3:4` |
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Answer» Correct Answer - A `R prop (mv)/(q)` So, `R_(1):R_(2)=(m_1)/(m_2) xx (V_1)/(V_2) xx (q_2)/(q_1) = 1/2 xx 2/3 xx 2/1 = 4/3` `(R_1)/(R_2)=4/3` So, choice (a) is correct. |
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