Electromagnetic WavesMedium
Question
An electromagnetic wave travelling in x -direction is described by field equation $E_{y} = 300sin\omega\left( t - \frac{x}{c} \right)$.
If the electron is restricted to move in y -direction only with speed of $1.5 \times 10^{6}\text{ }m/s$ then ratio of maximum electric and magnetic forces acting on the electron is $\_\_\_\_$ .
Options
A.200
B.150
C.400
D.300
Solution
Sol. [Key Concept: Ratio of forces $\frac{F_{e}}{F_{m}} = \frac{E}{vB} = \frac{c}{v}$.]
$$E_{y} = 300sin\omega\left( t - \frac{x}{v} \right)$$
$$\begin{array}{r} F_{M} = qvB\#(i) \end{array}$$
$$\begin{array}{r} F_{e} = qE\#(ii) \end{array}$$
$$\frac{F_{e}}{F_{m}} = \frac{qE}{qvB} = \frac{E}{vB} = \frac{c}{v} = \frac{3 \times 10^{8}}{1.5 \times 10^{6}} = 200 $$
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