A particle of charge -16×10-18 C 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 Vm is along the negative z-axis. If the charged particle continues moving along the x-axis, the magnitude of B is 10n Wbm2. Then the value of n is _______.

The net force along z-axis is zero.qE→+qv→×B→=0 or, E→=-v→×B→=B→×v→ E=Bv ⇒ B=Ev ∵ B→⊥v→B=Ev=10410=103 Wbm2

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A particle of charge $- 16 \times 10^{- 18} C$ 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 $10^{4} \frac{V}{m}$ is along the negative $z -$ axis. If the charged particle continues moving along the $x -$ axis, the magnitude of $B$ is $10^{n} \frac{W b}{m^{2} .}$ Then the value of $n$ is $_______.$

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The net force along z-axis is zero.

$q \vec{E} + q (\vec{v} \times \vec{B}) = 0$

or, $\vec{E} = - (\vec{v} \times \vec{B}) = (\vec{B} \times \vec{v})$

$E = Bv \Rightarrow B = \frac{E}{v} [∵ \vec{B} ⊥ \vec{v}]$

$B = \frac{E}{v} = \frac{10^{4}}{10} = 10^{3} \frac{Wb}{m^{2}}$

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