Question


A particle of charge 16×1018 coulomb moving with velocity 10 ms1 along the x-axis enters a region where a magnetic field of induction B is along the y -axis, and an electric field of induction B is along the y-axis, and an electric field of magnitude 104V/m is along the negative z-axis. lf the charged particle continues moving along the x-axis, the magnitude of B is

A
103Wb/m2
B
105Wb/m2
C
1016Wb/m2
D
103Wb/m2
Solution
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Particle travels along x axis
Hence Vy=Vz=0
Electric feild is along the negative z axis
Ex=Ey=0
Therefore net force on the particle F=q(E+V×B)
Resolve the motion along three coordinate axis
ax=Fxm=qm(Ex+VyBzVxBy)ay=Fxm=qm(Ey+VzBxVxz)az=Fxm=qm(Ez+VxByVyBx)
Since,
Vy=Vz=0Ex=Ey=0Bx=Bz=0
ax=ay=0az=qm(Ez+VxBy)
Again az=0 , as the particle transverse through the region undeflected
Ez=VxBy
By=EzVx=10410=103wb/m2

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