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(ik)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)T
Magnetic Force (¯F) on charged particle (q) moving with Velocity (V) in magnetic field (¯B) is given as
¯F=q(¯VׯB)
Case 1: q(^j+^k)=q(^i×(Bx^i+By^j+Bz^k))
^j+^k=By^kBz^j
Bz=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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