A light beam is described by E = 800 sin ω (t - x/c). An electron is allowed to move normal to the propagation of light beam with a speed of 3 × 107 ms ⁻¹. What is the maximum magnetic force exerted on the electron? (a) 1.28 × 10 - 18 N (b) 1.28 × 10 - 21 N (c) 12.8 × 10 - 17 N (d) 12.8 × 10 - 18 N

Answer: (d). Peak magnetic field B₀ = E₀/c = 8003 × 10⁸ = 2.67 × 10⁻⁶ T. Maximum magnetic force (velocity normal to B): F = evB₀. F = 1.6 × 10⁻¹⁹ × 3 × 10⁷ × 2.67 × 10⁻⁶ = 1.28 × 10⁻¹⁷ N. So the answer is (d) 12.8 × 10⁻¹⁸ N.

A light beam is described by E = 800 sin ω (t - x/c). An electron is… | JEE Main 2021 (26 Aug, Shift 2)

Q46JEE Main 2021 · 26 AUG · SHIFT 2Medium

Nature of EM Waves & Wave Equation

A light beam is described by $E = 800 \sin \omega \left(t - \frac{x}{c}\right)$ . An electron is allowed to move normal to the propagation of light beam with a speed of 3 $\times$ 107 ms ${}^{-1}$ . What is the maximum magnetic force exerted on the electron?

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Answer: (d)

Peak magnetic field $B_0 = \dfrac{E_0}{c} = \dfrac{800}{3 \times 10^{8}} = 2.67 \times 10^{-6}$ T.
Maximum magnetic force (velocity normal to $B$ ): $F = evB_0$ .
$F = 1.6 \times 10^{-19} \times 3 \times 10^{7} \times 2.67 \times 10^{-6} = 1.28 \times 10^{-17}$ N.
So the answer is (d) $12.8 \times 10^{-18}$ N.

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Nature of EM Waves & Wave Equation question from JEE Main 2021 (26 Aug, Shift 2)

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