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Q.

Figure shows two large cylindrical shells having uniform linear charge densities +λ  and λ . Radius of inner cylinder is ‘a’ and that of outer cylinder is ‘b’. A charged particle of mass m, charge q revolves in a circle of radius r. Then, its speed ‘v’ is: (Neglect gravity and assume the radii of both the cylinders to be very small in comparison to their length.)

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a

2λqπε0m

b

λq2πε0m

c

λq4πε0m

d

λqπε0m

answer is A.

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Detailed Solution

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Using Gauss's law for Gaussian surface shown in figure.  
E.dA=qinε0

E. 2πrl=λlε0 ;

E = λ2πε0r

For circular motion,  
qE =mV2r=2πε0r

V =2πε0m

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Figure shows two large cylindrical shells having uniform linear charge densities +λ  and −λ . Radius of inner cylinder is ‘a’ and that of outer cylinder is ‘b’. A charged particle of mass m, charge q revolves in a circle of radius r. Then, its speed ‘v’ is: (Neglect gravity and assume the radii of both the cylinders to be very small in comparison to their length.)