Question

Magnetic field at the centre of a circular loop of area 'A' is 'B'. The magnetic moment of the loop will be (µ₀ = permeability of free space) ____________.

Options

• `"BA"^(3/2)/(mu_0pi)`

• `"BA"^(3/2)/(mu_0pi^(1/2)`

• `(2"BA"^(3/2))/(mu_0pi^(1/2)`

• `(2"BA"^2)/(mu_0pi)`

Answer 1

Magnetic field at the centre of a circular loop of area 'A' is 'B'. The magnetic moment of the loop will be (µ₀ = permeability of free space) `(2"BA"^(3/2))/(mu_0pi^(1/2)`.

Explanation:

If r is the radius of the circular loop them the area of the loop `"A" = pi "r"^2`

`therefore "r" = sqrt ("A"/pi)`

∴ The magnetic field at the centre is given by

`"B" = (mu_0 "I")/(2"r") = (mu_0 "I")/(2 sqrt("A"/pi))`

`therefore "I" = (2"B")/mu_0 sqrt("A"/pi)`

Magnetic moment

`"M" = "IA" = (2"B")/mu_0 . sqrt ("A"/pi) . "A"`

`= (2"BA" ^(3//2))/(mu pi ^(1/2)`