Question

A particle of charge $-16\times {10}^{-18}\text{C}$ moving with velocity $10{\text{ms}}^{-1}$ along the X-axis enters region where a magnetic field of induction $B$ is along the Y-axis and an electric field of magnitude ${10}^4\text{V/m}$ is along the negative Z-axis. If the charged particle continues moving along the X-axis, the magnitude of $B$ is -

• A. ${10}^3{\text{Wb/m}}^2$
• B. ${10}^5{\text{Wb/m}}^2$
• C. ${10}^{16}{\text{Wb/m}}^2$
• D. ${10}^{-3}{\text{Wb/m}}^2$

Answer 1

The correct option is A ${10}^3{\text{Wb/m}}^2$

Charge particle continues to move along X-axis. It means force due to magnetic field and due to electric field are equal and opposite.

Since charge is negative, force due to electric field will be along positive Z-axis. Force due to magnetic field is along negative Z-axis.
Their magnitude should be equal.
$qE=qvB$
$\Rightarrow B=\frac{E}{v}$
$\Rightarrow B=\frac{{10}^4}{10}$
$B={10}^3\text{T}$