Q.

Two long concentric conducting cylinders with cross section as shown in figure have radii R and 2R.The inner one carries a charge per unit length. A particle of mass m and negative charge of magnitude q is projected at a velocity v0 perpendicular to common axis. The projection is done from a point at a distance 3R2from the axis of cylinders. Choose correct statement(s).

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a

Maximum v0 such that it does not touch the outer cylinder is 16qλ7πε0mln(43)

b

Maximum v0 such that it does not touch the outer cylinder is qλ2πε0m[1+2ln(43)]

c

If v0=qλ4πε0m then particle moves in a circular path

d

If v0=qλ2πε0m then particle moves in a circular path

answer is B, D.

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Detailed Solution

2kλqr=mv2r        λq2π0m=v

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3R22Rλq2π0rdr=λq2π0ln43

12mv02=12mλq2π0m+λ2π0ln43

v0=λq2π0m[1+2ln43]

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Two long concentric conducting cylinders with cross section as shown in figure have radii R and 2R.The inner one carries a charge per unit length. A particle of mass m and negative charge of magnitude q is projected at a velocity v0 perpendicular to common axis. The projection is done from a point at a distance 3R2from the axis of cylinders. Choose correct statement(s).