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An electron is released from the origin at a place where a uniform electric field E and a uniform magnetic field B exist along negative y axis and negative z axis respectively. Find the displacement of the electron along the y axis when it's velocity becomes perpendicular to the electric field for the first time .
Asked by prakriti12oct | 29 Jul, 2019, 12:12: AM
( Vector quantities are typed in Bold, i, j, k are unit vectors along the axis of cartesian coordinate system)

Electric field E = - i |E|   ;  Magnetic field B = - k |B| ; initial velocity  v = i |v|

Force on electron, F = e ( E + v×B ) = - i e |E| + j e |v| |B|

Hence force along y axis, Fy = (e v B )    and acceleration along y axis, ay = (e v B )/m

we know the equation for Displacement S ,  " S = ut +(1/2)at2 ",
where u is initial velocity which is zero here because electron is released , a is acceleration and t is time

hence displacement Sy of electron along y-axis as a function of time is given by,

Sy = (1/2) [ ( e v B )/m ] t2
Answered by Thiyagarajan K | 29 Jul, 2019, 08:11: AM
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