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Question

# A particle of charge −16 ×10−18 C moving with velocity 10 m/s along the X−axis enters region where a magnetic field of induction B is along Y−axis and field of magnitude 104 V/m is along the negative Z−axis. If the charged particle continuous moving along the X−axis, the magnitude of B is:

A
106 Wb/m2
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B
105 Wb/m2
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C
103 Wb/m2
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D
107 Wb/m2
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Solution

## The correct option is C 103 Wb/m2Given that,Particle of chargeq=1.6×10−19C Velocity v=10m/s Field induction B=104V/m Now, particle travel along x-axisThen, vy=vz=0 And field induction B is along y-axisThen, Bx=Bz=0 Electric field is along negative z-axisThen, Ex=Ey=0Now, net force on particle isF=q(→E+→v×→B) Resolve the motion along the three coordinates Fx=max ax=Fxm=qm(Ex+vyBz−vzBy) ay=qm(Ey+vzBx−vxBz) az=qm(Ez+vxBy−vxBy) So, Ex=Ey=0,vy=vz=0,Bx=Bz=0 Now, ax=ay=0 az=qm(−Ez+vxBy) Now, againaz=0 the particle traverse through the region un-deflected Ez=vxBy By=Ezvx By=10410 By=103wb/m2 Hence, the magnitude of B is 103wb/m2

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