An electromagnetic wave travelling in x-direction is described by field equation $\mathrm{E}_{\mathrm{y}}=300 \sin \omega\left(\mathrm{t}-\frac{\mathrm{x}}{\mathrm{c}}\right)$. If the electron is restricted to move in y-direction only with speed of $1.5 \times 10^{6} \mathrm{~m} / \mathrm{s}$ then ratio of maximum electric and magnetic forces acting on the electron is ____.

JEE Main · 2026 · 02 Apr 2026 · Shift 1 · EM Waves

An electromagnetic wave travelling in x-direction is described by field equation

E_{y} = 300 sin ω (t - \frac{x}{c})

. If the electron is restricted to move in y-direction only with speed of

1.5 \times 1 0^{6} m / s

then ratio of maximum electric and magnetic forces acting on the electron is ____.

(A)200✓ Correct
(B)150
(C)400
(D)300

Answer: (A)

Solution

The electric and magnetic forces on the electron have magnitudes

F_{e} = q E

and

F_{m} = q v B

, so

\frac{F _{e}}{F _{m}} = \frac{E}{v B}

. In an electromagnetic wave the field amplitudes obey

E = c B

, hence

\frac{F _{e}}{F _{m}} = \frac{c B}{v B} = \frac{c}{v} = \frac{3 \times 1 0 ^{8}}{1.5 \times 1 0 ^{6}} = 200

. The ratio of maximum electric to magnetic force is

200

JEE Main · 2026 · 02 Apr 2026 · Shift 1 · Single correct option

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