First slide

Introduction-Electromagnetic waves

Question

A beam of light travelling along x-axis is described by the electric field $E_{Y} = (300 V m^{- 1}) \sin ω (t - \frac{x}{C})$ . Calculate the maximum magnetic force on a charge $q = 4 e$ , moving along y-axis with a speed of $2 \times 10^{7} m / s$ is (where $e = 1.6 \times 10^{- 19} C$ )

Moderate

A

$0.64 \times 10^{- 16} N$
B

$1.28 \times 10^{- 17} N$
C

$0.32 \times 10^{- 16} N$
D

$0.32 \times 10^{- 17} N$

Solution

Amplitude of magnetic field is $B_{0} = \frac{E_{0}}{C} = \frac{300}{3 \times 10^{8}} = 1 \times 10^{- 6} T$
( From the given equation $E_{0} = 300 V / m$ )
Maximum magnetic force is
$F_{m} = q V B_{0} = 4 e V B_{0}$
$\Rightarrow F_{m} = 4 \times 1.6 \times 10^{- 19} \times 2 \times 10^{7} \times 1 \times 10^{- 6}$
$\Rightarrow F_{m} = 12.8 \times 10^{- 18} \Rightarrow F_{m} = 1.28 \times 10^{- 17} N$

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