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Q.

A charged dust particle of radius 5×10−7  m is moving in a horizontal electric field of intensity 6.28×105  V/m. The surrounding medium is air with coefficient of viscosity η=1.6×10−5  N−s/m2. If this particle is moving with a uniform horizontal speed of 0.02 m/s, the number of excess electrons on the drop are 6k. Find the value of k.

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answer is 5.

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Detailed Solution

As particle is moving horizontally, only forces acting on it are Stoke's force and electric force.If v=constant,  then  6πηv=qE⇒ 6πηrv=neE⇒n= 6πηrvEe=6×3.14×1.6×10−5×5×10−7×0.026.28×105×1.6×10−19=30=6k⇒k=5
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