First slide

Introduction-Electromagnetic waves

Question

A beam of light travelling along x-axis is described by the electric field $E_{Y} = (600 V m^{- 1}) \sin ω (t - \frac{x}{c})$ , then the maximum magnetic force on a charge $q = 2 e$ moving along y-axis with a speed of $3 \times 10^{7} m / s$ is (where $e = 1.6 \times 10^{- 19} C$ )

Moderate

A

$1.92 \times 10^{- 16} N$
B

$1.92 \times 10^{- 17} N$
C

$1.6 \times 10^{- 16} N$
D

$1.6 \times 10^{- 17} N$

Solution

Amplitude of magnetic field is $B_{0} = \frac{E_{0}}{C} = \frac{600}{3 \times 10^{8}} = 2 \times 10^{- 6} T$
( from the given equation, $E_{0} = 600 V / m$ )
Maximum magnetic force is $F = q v B_{0} = 2 e v B_{0}$
$\Rightarrow F = 2 \times 1.6 \times 10^{- 19} \times 3 \times 10^{7} \times 2 \times 10^{- 6}$
$\Rightarrow F = 1.92 \times 10^{- 17} N$

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