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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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Knowledge Check

  • 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

    A
    `(mu_(0)nI_(max)omega R^(2))/(2r) sin omega t`
    B
    `(2mu_(0)nI_(max)omega R^(2))/(r) sin omega t`
    C
    `(mu_(0)nI_(max)omega R^(2))/(3r) sin omega t`
    D
    `(3mu_(0)nI_(max)omega R^(2))/(2r) sin omega t`

  • The magnetic field inside a long straight solenoid carrying current

    A
    is zero
    B
    decreases as we move towards its end
    C
    increases as we move towards its end
    D
    is the same at all points

  • The magnetic field on the axis of a long solenoid having n turns per unit length and carrying a current is

    A
    `mu_(0)ni`
    B
    `mu_(0)n^(2)i`
    C
    `mu_(0)ni^(2)`
    D
    none of these

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