An insulating rod having linear charge density $λ = 40 μ C m^{- 1}$ and linear mass density $μ = 0.1 k g m^{- 1}$ is released from rest in a uniform electric field $E = 100 V m^{- 1}$ directed perpendicular to the rod. If speed of the rod after it has travelled a distance of 2 m is $x \times 10^{- 1} m / s$ . Find x.

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answer is 4.

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Detailed Solution

Arbitrarily take V=0 at the initial point. Then at distance d downfield, where L is the rod length, $V = - E d a n d u_{e} = - λ L E d$
${(K + u)}_{i} = {(K + u)}_{f}$
$\Rightarrow 0 + 0 = \frac{1}{2} u L υ^{2} - λ L E d \Rightarrow υ = \sqrt{\frac{2 λ E d}{μ}} \Rightarrow υ = \sqrt{\frac{2 (40 \times 10^{- 6} C m^{- 1}) (100 N C^{- 1}) (2 m)}{(0.1 k g m^{- 1})}} = 0.4 m s^{- 1}$