Question

A narrow electron beam passes undeviated through an electric field $E=3\times {10}^4\text{volt/m}$ and an overlapping magnetic field $B=2\times {10}^{-3}{\text{W/m}}^2$. If electric field and magnetic field are mutually perpendicular. The speed of the electrons is

• A. $0.67\times {10}^{-7}\text{m/s}$
• B. $60\text{m/s}$
• C. $10.3\times {10}^7\text{m/s}$
• D. $1.5\times {10}^7\text{m/s}$

Answer 1

The correct option is D $1.5\times {10}^7\text{m/s}$

Given:
$E=3\times {10}^4\text{V/m}$
$B=2\times {10}^3{\text{Wb/m}}^2$
According to question
Electric force = Magnetic force
$eE=evB$
$\Rightarrow v=\frac{E}{B}=\frac{3\times {10}^4}{2\times {10}^{-3}}=1.5\times {10}^7\text{m/s}$
Hence option $\left(C\right)$ is correct.