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The magnetic field bar(dB) due to a smal...

The magnetic field `bar(dB)` due to a small current element `bar(dl)` at a distance `vec(r)` and carrying current `'I'` is

A

`bar(dB) = mu_0/(4π) i([bar(dl)×bar(r)]/r)`

B

`bar(dB) = mu_0/(4π) i^2([bar(dl)×bar(r)]/r)`

C

`bar(dB) = mu_0/(4π) i([bar(dl)×bar(r)]/r^2)`

D

`bar(dB) = mu_0/(4π) i([bar(dl)×bar(r)]/r^3)`

Text Solution

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The correct Answer is:
D
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Write using Biot-Savart law, the expression for the magnetic field vecB due to an element vecdl carrying current I at a distance vecr from it in vector form. Hence, derive the expression for the magnetic field due to a current loop of radius R at a point P distant x from its centre along the aixs of the loop.

Knowledge Check

  • The magnetic field dvecB due to a small current element dvecl at a distance vecr and element carrying current i is,

    A
    `dvecB=mu_(0)/(4pi)i((dveclxxvecr)/(r))`
    B
    `dvecB=mu_(0)/(4pi)i^(2)((dveclxxvecr)/(r))`
    C
    `dvecB=mu_(0)/(4pi)i^(2)((dveclxxvecr)/(r^(2)))`
    D
    `dvecB=mu_(0)/(4pi)i((dveclxxvecr)/(r^(3)))`

  • The magnetic field vec(dB) due to a small current element vec(dl) carrying a current I at a distance vecr is given as

    A
    `vec(dB) = (mu_0)/(4pi) I[(vec(dI) xx vec(r))/(r)]`
    B
    `vec(dB) = (mu_0)/(4pi) I^2[(vec(dl) xx vec(r))/(r)]`
    C
    `vec(dB) = (mu_0)/(4pi) I^2[(vec(dl) xx vec(r))/(r^2)]`
    D
    `vec(dB) = (mu_0)/(4pi) I[(vec(dl) xx vec(r))/(r^3)]`

  • The magnetic field due to a bar magnet _____

    A
    has the same direction at any point
    B
    is uniform
    C
    is non-uniform
    D
    does not exist

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