A beam of light travelling along X-axis is described by the electric field $\mathrm{E}_{\mathrm{y}}=900 \sin \omega(\mathrm{t}-\mathrm{x} / \mathrm{c})$. The ratio of electric force to magnetic force on a charge q moving along Y-axis with a speed of $3 \times 10^{7} \mathrm{~ms}^{-1}$ will be : [Given speed of light $=3 \times 10^{8} \mathrm{~ms}^{-1}$]

JEE Main · 2022 · 27 Jul 2022 · Shift 1 · EM Waves

A beam of light travelling along X-axis is described by the electric field

E_{y} = 900 sin ω (t - x / c)

. The ratio of electric force to magnetic force on a charge q moving along Y-axis with a speed of

3 \times 1 0^{7} ms^{- 1}

will be :
[Given speed of light

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

]

(A) $1 : 1$
(B) $1 : 10$
(C) $10 : 1$ ✓ Correct
(D) $1 : 2$

Answer: (C)

Solution

The electric force on the charge is

F_{E} = q E_{0}

and the magnetic force is

F_{B} = q v B_{0}

. For an EM wave,

E_{0} / B_{0} = c

, so the ratio

F_{E} / F_{B} = E_{0} / (v B_{0}) = c / v = (3 \times 1 0^{8}) / (3 \times 1 0^{7}) = 10

. Hence the ratio is

10 : 1

JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Single correct option

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