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 $\overrightarrow{\mathrm{E}}=30 \hat{\mathrm{j}} \sin \left(1.5 \times 10^{7} \mathrm{t}-5 \times 10^{-2} \mathrm{x}\right) \mathrm{V} / \mathrm{m}$. The maximum magnetic force experienced by the electron will be: (given $\mathrm{c}=3 \times 10^{8} \mathrm{~ms}^{-1}$ and electron charge $=1.6 \times 10^{-19} \mathrm{C}$)

(D) $4.8 \times 10^{-19} \mathrm{~N}$

(A) $3.2 \times 10^{-18} \mathrm{~N}$

(B) $1.5 \times 10^{-19} \mathrm{~N}$

(C) $2.4 \times 10^{-18} \mathrm{~N}$

JEE Main · 2020 · 05 Sep 2020 · Shift 1 · EM Waves

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

E = 30 \hat{j} sin (1.5 \times 1 0^{7} t - 5 \times 1 0^{- 2} x) V / m

. The maximum magnetic force experienced by the electron will be: (given

c = 3 \times 1 0^{8} ms^{- 1}

and electron charge

= 1.6 \times 1 0^{- 19} C

)

(A) $3.2 \times 1 0^{- 18} N$
(B) $1.5 \times 1 0^{- 19} N$
(C) $2.4 \times 1 0^{- 18} N$
(D) $4.8 \times 1 0^{- 19} N$ ✓ Correct

Answer: (D)

Solution

The wave's magnetic amplitude is

B_{0} = \frac{E _{0}}{c} = \frac{30}{3 \times 1 0 ^{8}} = 1 0^{- 7}

T. The electron moves along

y

v = 0.1 c = 3 \times 1 0^{7}

m/s, so the greatest magnetic force it can feel is

F = q v B_{0} = (1.6 \times 1 0^{- 19}) (3 \times 1 0^{7}) (1 0^{- 7}) = 4.8 \times 1 0^{- 19}

JEE Main · 2020 · 05 Sep 2020 · Shift 1 · Single correct option

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JEE Main · 2020 · 05 Sep 2020 · Shift 1 · EM Waves

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