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=1i^m/s. The force becomes F=q(i−k)N when the velocity is changed to v2=1j^m/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
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Updated on : 2022-09-05
Solution
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Correct option is A)
Let the magnetic induction at required point be
Bˉ=(Bxi^+Byj^+Bzk^)T
Magnetic Force (Fˉ) on charged particle (q) moving with Velocity (V) in magnetic field (Bˉ) is given as
Fˉ=q(Vˉ×Bˉ)
Case 1: q(−j^+k^)=q(i^×(Bxi^+Byj^+Bzk^))
−j^+k^=Byk^−Bzj^
Bz=1....(i)
By=+1....(ii)
Case 2: q(j^−k^)=q(j^(Bxi^+Byj^+Bzk^))
∴j^−k^=−Bxk^+Bzi^
∴Bx=1....(iii)
From (i),(ii)&(iii)
Bˉ=(i^+j^+k^)T Thus, option A
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