Question

An electron is constrained to move along the$y$-axis with a speed of $0.1c$ ($c$ is the speed of light) in the presence of electromagnetic wave, whose electric field is$E=30j\sin (1.5\times {10}^{7}t–5\times {10}^{-2}x)V/m$. The maximum magnetic force experienced by the electron will be : (given $c=3\times {10}^{8}m{s}^{-1}$and electron charge = $1.6\times {10}^{-19}C$)

• A. $2.4\times {10}^{-18}N$
• B. $4.8\times {10}^{-19}N$
• C. $3.2\times {10}^{-18}N$
• D. $1.6\times {10}^{-19}N$

Answer 1

The correct option is B

$4.8\times {10}^{-19}N$

Step 1. Given data:

The velocity of electrons along $y$-axis, $v_e=0.1C$

EM wave is along $x$ axis$E=30j\sin (1.5\times {10}^{7}t–5\times {10}^{-2}x)V/m$

Speed of EM wave, $c=3\times {10}^{8}m{s}^{-1}$

Electric charge $1.6\times {10}^{-19}C$

Step 2. Force experienced by electron:

The electric field is given by, $E=v\times B$

Where $E$ is the Electric field and $B$ is the magnetic field

$v$ is the velocity

The maximum electric field is when the magnetic field is perpendicular to the direction of velocity or propagation, $E=cB\Rightarrow B=E/c=\frac{30}{c}$

The maximum force corresponding to the maximum field is will be, $F_{max}=qvB$

$F_{max}=1.6\times {10}^{-19}\times 0.1\times c\times \frac{30}{c}$

$F_{max}=4.8\times {10}^{-19}N$.

Hence, option B is correct.