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What is the magnetic moment of a current...

What is the magnetic moment of a current carrying thin circular loop if the radius of the loop is equal to R and the magnetic induction at its centre is equal to B ?

A

`(2piBR^(3))/mu_(0)`

B

`(4pi BR^(3))/mu_(0)`

C

`(BR^(2))/mu_(0)`

D

`(pi BR^(3))/mu_(0)`

Text Solution

Verified by Experts

The correct Answer is:
A
Magnetic moment `M=IA =I (pi R^(2))` ...(1)
But magnetic field at the centre of a circular coil carrying a current is `B=mu_(0)/(4pi)((2pi I)/R)=(mu_(0)I)/(2 R)`
`:. I=(2BR)/mu_(0)` ...(2)
Using (2) in (1), we get
`M=(2 BR)/mu_(0) xxpi R^(2) :. M =(2pi BR^(3))/mu_(0)`
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Knowledge Check

  • Find the magnetic moment of a thin round loop with current if the radius of the loop is equal to r and the magnetic induction at its centre is equal to X.

    A
    `(Xr^(2))/(mu_(0))`
    B
    `(3 pi Xr^(3))/(mu_(0))`
    C
    `(2 pi X r^(3))/(mu_(0))`
    D
    `(4 pi x r^(3))/(mu_(0))`

  • 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 at the centre of a current carrying circular loop is B. If the radius of the loop is doubled, keeping the current same, the magnetic field at the centre of the loop would be :

    A
    `B/4`
    B
    `B/2`
    C
    2 B
    D
    4 B

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