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 E → t = E 0 sin ⁡ ω t i ^ where E 0 = 1.0 N C - 1 and ω = 10 3 rad s - 1 . Consider the effec

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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 E → t = E 0 sin ⁡ ω t i ^ where E 0 = 1.0 N C - 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 ____________.

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Correct answer: 2

m = 10 - 3 kg q = 1 C t = 0 Force on particle will be F = q E = q E 0 sin ⁡ ω t At v m a x , F = 0 ⇒ q E 0 sin ⁡ ω t o = 0 ⇒ w t o = π F = q E 0 sin ⁡ ω t d v d t = q E 0 m sin ⁡ ω t ∫ 0 v d v = ∫ 0 π ∕ ω q E 0 m sin ⁡ ω t d t v - 0 = q E 0 m ω - cos ⁡ ω t 0 π ∕ ω v - 0 = q E 0 m ω - cos ⁡ π - - cos ⁡ 0 v = 1 × 1 m ω × 2 = 2 m/s = 2.00

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