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A long solenoid of radius 2R contains an...

A long solenoid of radius `2R` contains another coaxial solenoid of radius `R`. The coils have the same number of turns per unit length and initially both carry zero current. At time, `t=0`, current start increasing linearly with time in both solenoids. At any moment the current flowing in the inner coil is twice as large as that in the outer one and their directions are same. A charged particle, initially at rest between the two solenoids, start moving along a circular trajectory due to increasing current in the solenoid as shown in the figure What is the radius of the circle ? (Assume magnetic field due to each solenoid remains uniform over its cross-section.)

A

`sqrt(2)R`

B

`sqrt(3)R`

C

`(3)/(2)R`

D

none of these

Text Solution

Verified by Experts

Current at time `t` in outer coil is `I=kt`, and inner coil `2I=2kt`
Flux enclosed by particle's trajectory of radius `r` is `phi=piR^(2)xx2B+pixxr^(2)xxB=(2R^(2)+r^(2))pimu_(0)nkt`
`Exx2pi r=(2R^(2)+r^(2))pi mu_(0)nk`
`(mv^(2))/(r )=qvB`
`v=(qE)/(m)t`
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