A particle, of mass 10 -3 kg and charge 1.0 C , is initially at rest. At time t =0 , the particle comes under the influence of an electric field overrightarrow E ( t )= E 0 sin ω t hat i , where E 0 =1.0 NC -1 and ω=10 3 rad s -1 . Consider the effect of only the electrical force on the particle. Then the maximum speed, in m s -1 , attained by the particle at subsequent times is \ \ \ \ .

Physics · Moving Charges and Magnetic Field

JEE Advanced 2018 — Paper 2 — Question 8

A particle, of mass $10^{-3} \mathrm{~kg}$ and charge 1.0 C , is initially at rest. At time $\mathrm{t}=0$ , the particle comes under the influence of an electric field $\overrightarrow{\mathrm{E}}(\mathrm{t})=\mathrm{E}_{0} \sin \omega \mathrm{t} \hat{\mathrm{i}}$ , where $\mathrm{E}_{0}=1.0 \mathrm{NC}^{-1}$ and $\omega=10^{3} \mathrm{rad} \mathrm{s}^{-1}$ . Consider the effect of only the electrical force on the particle. Then the maximum speed, in $\mathrm{m} \mathrm{s}^{-1}$ , attained by the particle at subsequent times is $\_\_\_\_$ .

Answer: 2

Numerical answer — enter this value.

Step-by-step solution

$m \frac{d v}{d t}=q E$

$\int_{0}^{v} d v=\frac{q E_{0}}{m} \int_{0}^{t} \sin \omega t d t$

$\mathrm{v}=\frac{\mathrm{qE}_{0}}{\mathrm{~m}} \frac{(1-\cos \omega \mathrm{t})}{\omega}=\frac{1 \times 1(1-\cos \omega \mathrm{t})}{10^{-3} \times 10^{3}}$

$\mathrm{v}=(1-\cos \omega \mathrm{t})$

$\therefore \mathrm{v}_{\text {max }}=2 \mathrm{~m} / \mathrm{s}$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2018
Paper: Paper 2
Subject: Physics
Chapter: Moving Charges and Magnetic Field
Topic: Motion of Charged Particles in Combined Electric and Magnetic Fields