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 = 30j sin (1.5 × 10⁷ t - 5 × 10⁻² x) V/m. The maximum magnetic force experienced by the electron will be: (given c = 3 × 108 ms–1 and electron charge = 1.6 × 10–19 C) (a) 4.8 × 10–19 N (b) 2.4 × 10–18 N (c) 3.2 × 10–18 N (d) 1.6 × 10–18 N

Answer: (a). B₀ = E₀/c = 303 × 10⁸ = 10⁻⁷ T, along k (wave along x, E along y). Electron velocity v = 0.1c = 3 × 10⁷ m/s along y, perpendicular to B. Fmax = evB₀ = 1.6 × 10⁻¹⁹ × 3 × 10⁷ × 10⁻⁷ = 4.8 × 10⁻¹⁹ N. So the answer is (a) 4.8 × 10⁻¹⁹ N.

An electron is constrained to move along the y-axis with a speed of… | JEE Main 2020 (5 Sep, Shift 1)

Q57JEE Main 2020 · 5 SEP · SHIFT 1Medium

Nature of EM Waves & Wave Equation

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

$\vec{E} = 30\hat{j} \sin\left(1.5 \times 10^{7} t - 5 \times 10^{-2} x\right)$ V/m.

The maximum magnetic force experienced by the electron will be:

(given c = 3 $\times$ 108 ms–1 and electron charge = 1.6 $\times$ 10–19 C)

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Answer: (a)

$B_0 = \dfrac{E_0}{c} = \dfrac{30}{3 \times 10^{8}} = 10^{-7}$ T, along $\hat{k}$ (wave along $x$ , $E$ along $y$ ).
Electron velocity $v = 0.1c = 3 \times 10^{7}$ m/s along $y$ , perpendicular to $B$ .
$F_{max} = evB_0 = 1.6 \times 10^{-19} \times 3 \times 10^{7} \times 10^{-7} = 4.8 \times 10^{-19}$ N.
So the answer is (a) $4.8 \times 10^{-19}$ N.

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Nature of EM Waves & Wave Equation question from JEE Main 2020 (5 Sep, Shift 1)

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