A particle of charge $16\times {10}^{-16}$ moving with velocity $10{\mathrm{ms}}^{-1}$along x-axis enters a region where magnetic field of induction $\overline{\mathrm{B}}$ is along the y-axis and an electric field of magnitude ${10}^4{\mathrm{Vm}}^{-1}$ is along the negative z-axis. If the charged particle continues moving along x-axis, the magnitude of $\overline{\mathrm{B}}$ is:

Given data:

$\mathrm{charge} \mathrm{of} \mathrm{particle} 16\times {10}^{-16}, \mathrm{velocity} 10{ \mathrm{ms}}^{-1}, \mathrm{field} \mathrm{of} \mathrm{magnitude} {10}^4{\mathrm{Vm}}^{-1}.$ 

Concept used: moving charges and magnetism

Detailed solution:

Since the trajectory of the particle remains unaltered, 

Net force on the particle is zero. 

I.e Lorentz force

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

From the given data

$(16\times {10}^{-16})\left[-{10}^{-4}\hat{k}+(10\hat{i}\times B\hat{j})\right] = 0$

On solving the above equation

$B=1\times {10}^3 Wb{m}^{-2}$