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A long solenoid of radous R has n turns ...

A long solenoid of radous `R` has `n` turns of wire per unit length and carries a time-varying current that varies sinusiodally as `I = I_(max) cos omegat`, where `I_(max)` is the maximum current and `omega` I the angular frequancy of the alternating current source (shows in Fig.)

The magnitude of the induced electric field inside tha solenoid, a distance `r lt R` from its long central axis is

A

`(3 mu_(0)nI_(max)omega)/(2) r sin omega t`

B

`(mu_(0)nI_(max)omega)/(2) r cos omega t`

C

`mu_(0)nI_(max)omega r sin omega t`

D

`(mu_(0)nI_(max)omega)/(2) r sin omega t`

Text Solution

Verified by Experts

The correct Answer is:
D
`E = (r )/(2) (dB)/(dt) = (r )/(2) mu_(0)n (dI)/(dt) rArr E = - (mu_(0)nr)/(2) I_(max) omega sin omega t`
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A long solenoid of radous R has n turns of wire per unit length and carries a time-varying current that varies sinusiodally as I = I_(max) cos omegat , where I_(max) is the maximum current and omega I the angular frequancy of the alternating current source (shows in Fig.) The magnitude of electric field outside the solenoid at a distance r gt R from its long central axis is

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Knowledge Check

  • A 90 cm long solenoid has six layers of windings of 450 turns each. If the diameter of solenoid is 2.2 cm and current carried is 6 A, then the magnitude of magnetic field inside the solenoid, near its centre is

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    `50 pi G`
    B
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    C
    `72 pi G`
    D
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  • Current flowing through a long solenoid is varied. Then, magnetic flux density of the magnetic field inside it varies :

    A
    inversely with I
    B
    inversely with`I^(2)`
    C
    directly with I
    D
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