Question

# A charged particle having charge q experiences a force →F=q(−→j+→k)N in a magnetic field B when it has a velocity v1=1^i m/s. The force becomes →F=q(→i−→k)N when the velocity is changed to v2=1^jm/sec. The magnetic induction vector at that point is :

A
(^i+^j+^k) T
B
(^i^j^k) T
C
(^i^j+^k) T
D
(^i+^j^k) T
Solution
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#### Let the magnetic induction at required point be ¯B=(Bx^i+By^j+Bz^k)TMagnetic Force (¯F) on charged particle (q) moving with Velocity (V) in magnetic field (¯B) is given as ¯F=q(¯V×¯B)Case 1: q(−^j+^k)=q(^i×(Bx^i+By^j+Bz^k))−^j+^k=By^k−Bz^jBz=1....(i)By=+1....(ii)Case 2: q(^j−^k)=q(^j(Bx^i+By^j+Bz^k))∴^j−^k=−Bx^k+Bz^i∴Bx=1....(iii)From (i),(ii)&(iii)¯B=(^i+^j+^k)T Thus, option A

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