Consider a particle of mass 1 gm and charge 1.0 Coulomb is at rest. Now the particle is subjected to an electric field E(t)=E_0 sin ω t in the x -direction, where E_0=2 Newton/Coulomb and ω=1000 rad / sec . The maximum speed attained by the particle is

Correct answer: (B) 4 m/sec. V_max =1/m ∫_0^T/2 F d t,=1/m ∫_0^T/2 q E_0 sin (ω t) d t =(2 qE_0)/(~m ω)=4 ~m / s

Q144 / 155 · WBJEE 2025 · Physics

Consider a particle of mass 1 gm and charge 1.0 Coulomb is at rest. Now the particle is subjected to an electric field $E(t)=E_0 \sin \omega t$ in the $x$-direction, where $E_0=2$ Newton/Coulomb and $\omega=1000 \mathrm{rad} / \mathrm{sec}$. The maximum speed attained by the particle is

A
2 m/sec
Correct answer
B
4 m/sec
C
6 m/sec
D
8 m/sec

Solution

$V_{\max }=\frac{1}{m} \int_0^{\frac{T}{2}} F d t,=\frac{1}{m} \int_0^{\frac{T}{2}} q E_0 \sin (\omega t) d t$ $=\frac{2 \mathrm{qE}_0}{\mathrm{~m} \omega}=4 \mathrm{~m} / \mathrm{s}$

Hence, the correct answer is option: 'B'.

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