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 $\vec{E}(t)=E_{0} \sin \omega t \hat{\imath}$, where $E_{0}=1.0 NC^{-1}$ and $\omega=10^{3} rad s^{-1}$. 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 ____.

JEE Advanced · 2018 · 20 May 2018 · Paper 2 · Electrostatics

A particle, of mass

1 0^{- 3} k g

and charge

1.0 C

, is initially at rest. At time

t = 0

, the particle comes under the influence of an electric field

E (t) = E_{0} sin ω t \overset{}{^}

, where

E_{0} = 1.0 N C^{- 1}

and

ω = 1 0^{3} r a d 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 ____.

Answer: 2

Solution

The force on the particle is

F = q E_{0} sin ω t

. Using

m \frac{d v}{d t} = q E_{0} sin ω t

and integrating:

v = \frac{q E _{0}}{mω} (1 - cos ω t)

. The maximum speed occurs when

cos ω t = - 1

, giving

v_{ma x} = \frac{2 q E _{0}}{mω} = \frac{2 \times 1.0 \times 1.0}{1 0 ^{- 3} \times 1 0 ^{3}} = 2.0

m/s.

JEE Advanced · 2018 · 20 May 2018 · Paper 2 · Numerical answer

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