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Q.

A particle, of mass 10−3kg and charge 1.0C, is initially at rest. At time  t=0, the particle comes under the influence of an electric field  Et=E0sinωt i⌢, where E0=1.0N/C  and  ω=103rad/s. Consider the effect of only the electrical force on the particle. Then the maximum speed, in m/s , attained by the particle at subsequent times is   .

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Detailed Solution

m=10−3kg q=1C t=0 E=E0sin⁡ωt Force on particle will be  F=qE=qE0sin⁡ωt At mean position, speed id Vmax, and, F=0⇒qE0sin⁡ωt=0⇒ωt=π⇒t=πω Now, F=qE0sin⁡ωt⇒dVdt=qE0msin⁡ωt⇒∫0v dv=∫0π/ω qE0msin⁡ωtdt⇒V−0=qE0mω[−cos⁡ωt]0π/ω⇒V−0=qE0mω[(−cos⁡π)−(−cos⁡0)]⇒V=1×110−3103×2=2m/s
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