A particle of charge -16×10-18 coulomb moving with velocity 10 ms-1 along the x-axis enters a r

Question

A particle of charge -16&#215;10-18 coulomb moving with velocity 10 ms-1 along the x-axis enters a region where a magnetic field of induction B is along the y-axis, and an electric field of magnitude 104 V/m is along the negative z-axis. If the charged particle continues moving along the x-axis, the magnitude of B is

Accepted Answer

.....(1)
The solution of this problem can be obtained by resolving the motion along the three coordinate axes namely
a_x =

(E_x + v_yB_z - v_zB_y)
a_y =

(E_y + v_zB_x - v_xB_z)
a_z =

(E_z + v_xB_y - v_yB_z)
For the given problem,
E_x = E_y = 0, V_y = v_z = 0 and B_x = B_z = 0
Substituting in equation (2), we get
a_x = a_z = 0 and a_y = E_y - v_xB_z
If the particle passes through the region undeflected ay is also zero, then
E_y = v_xB_z
⇒ B_z = = 10³ Wb/m²

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