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(a) State Bio-Savart's law in vector for...

(a) State Bio-Savart's law in vector form expressing the magnetic field due to an element `vecdl` carrying current I at a distance r from the element.
(b) Write the expression for the magnitude of the magnetic field at the centre of a circular loop of radius 'R' carrying a steady current I. Draw the field lines due to the current loop.

Text Solution

Verified by Experts

(b) The magnitude of magnetic field is given as `B = (mu_0 I)/(2R)`
Field lines have been drawn in fig.
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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

  • Magnetic field intensity H at the centre of a circular loop of radius r carrying current I e.m.u. is

    A
    `(r )/(I)` oersted
    B
    `(2pi)/(r )` oersted
    C
    `(I)/(2pi r)` oersted
    D
    `(2pi r)/(I)` oersted

  • What will be magnetic field at centre of current carrying circular loop of radius R?

    A
    `(mu_(0)I)/(4piR)`
    B
    `(mu_(0)I)/(2piR)`
    C
    `(mu_(0)I)/(2R)`
    D
    zero

  • 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)]`

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    State Biot- Savart law. Use to obtain the magnetic field at a point due to a long, staright current carrying wire.

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