Question 116: EM waves

Question

An electron is constrained to move along
the y-axis with a speed of 0.1 c (c is the
speed of light) in the presence of
electromagnetic wave, whose electric
field is
$$\overrightarrow E  = 30\widehat j\sin \left( {1.5 	imes {{10}^7}t - 5 	imes {{10}^{ - 2}}x} ight)$$ V/m.
The maximum magnetic force experienced by
the electron will be :
(given c = 3 $$ 	imes $$ 108 ms–1 and electron charge =
1.6 $$ 	imes $$ 10–19 C)

Accepted Answer

$$
 \overrightarrow E  = 30\widehat j\sin (1.5 	imes {10^7}t - 5 	imes {10^{ - 2}}x)V/m$$
V = $${{1.5 	imes {{10}^2}} \over {5 	imes {{10}^{ - 2}}}}$$ = 3 $$ 	imes $$ 10
8
= C
$$ \Rightarrow B = E/C = {{30} \over {1.5 	imes {{10}^7}}} 	imes 5 	imes {10^{ - 2}}$$
$$ = {10^{ - 7}}Tesla$$
$$ \Rightarrow {F_{max}} = q\left( {\overrightarrow V  	imes \overrightarrow B } ight) = \left| {qVB} ight|$$
$$ = 1.6 	imes {10^{ - 19}} 	imes 0.1 	imes 3 	imes {10^8} 	imes {10^{ - 7}}$$
$$ = 4.8 	imes {10^{ - 19}}N$$

Answer

4.8 $$ 	imes $$ 10–19 N

Answer

2.4 $$ 	imes $$ 10–18 N

Answer

3.2 $$ 	imes $$ 10–18 N

Answer

1.6 $$ 	imes $$ 10–18 N

EM waves

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