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# A charged particle q is moving with a velocity →v1=2^im/s at a point in a magnetic field →B and experiences a force →F1=q(^k−2^j)N. If the same charge moves with velocity →v2=2^jm/s from the same point in that magnetic field and experiences a force →F2=q(2^i+^k)N, the magnetic induction at that point will be :−12^i+12^j+^k^i+12^j−12^k12^i+12^j+^k−12^i+^j+12^k

A
^i+12^j12^k
B
12^i+12^j+^k
C
12^i+12^j+^k
D
12^i+^j+12^k
Solution
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#### Let the magnetic induction at required point be ¯B=Bx^i+By^j+Bz^kMagnetic force (¯F) on particle of charge (q), moving with velocity ¯V in the magnetic field region of intensity (¯B) is given as¯F=q(¯V×¯B)Case 1: ¯F1=q(¯V1×¯B)q(^k−2^j)=q(2^i×(Bx^i+By^j+Bz^k))^k−2^j=2By^k−2Bz^j∴2By=1,By=1/2.....(i)−2=−2Bz,∴Bz=1.....(ii)Case 2: ¯F2=q(¯V2×¯B)q(2^i+^k)=q(2^j×(Bx^i+By^j+Bz^k))2^i+^k=−2Bx^k+2Bz^i∴−2Bx=1,∴+Bx=1/2......(iii)Thus from (i),(ii)&(iii)¯B=−12^i+12^j+^k

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