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Q.

In a cylindrical region of radius R, there exists a time varying magnetic field B such that dBdt=k(>0). A charged particle having charge q is placed at the point P at a distance d (> R) from its centre O. Now, the particle is moved in the direction perpendicular to OP (see figure) by an external agent upto infinity so that there is no gain in kinetic energy of the charged particle. Choose the correct statement/s.

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a

Work done by external agent is qπR24k if d=2R

b

Work done by external agent is qπR28k if d=4R

c

Work done by external agent is qπR24k if d=4R

d

Work done by external agent is qπR24k if d=6R

answer is A.

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Detailed Solution

∫E→⋅dI→=AdBdtE2πx2+d2=πR2kE=πR2k2x2+d2Wext =∫0∞ qE→⋅dx=qπR24k

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In a cylindrical region of radius R, there exists a time varying magnetic field B such that dBdt=k(>0). A charged particle having charge q is placed at the point P at a distance d (> R) from its centre O. Now, the particle is moved in the direction perpendicular to OP (see figure) by an external agent upto infinity so that there is no gain in kinetic energy of the charged particle. Choose the correct statement/s.