Question

Two short magnets of equal dipole moments M are fastened perpendicularly at their centre in the Figure . The magnitude of the magnetic field at a distance d from the centre on the bisector of the right angle is

Options

• `(u_0)/(4pi) M/d^3`

• `(u_0)/(4pi) (sqrt2M)/d^3`

• `(u_0)/(4pi) (2sqrt2M)/d^3`

• `(u_0)/(4pi) (2M)/d^3`

Answer 1

`(u_0)/(4pi) (2sqrt2M)/d^3`

Magnetic field (B₁) due to the short dipole A of dipole moment M at an axial point  is given by,

`vec B_1 = (u_0)/(4pi) (2M)/d^3`         ....(1)

Magnetic field (B₂) due to the short dipole B of dipole moment M at an axial point is given by,

`vec B_2 = (u_0)/(4pi) (2M)/d^3`         ....(2)

Resultant magnetic field (B) will be,

`B = sqrt (B_1^2 + B_2^2)`

B = `(u_0)/(4pi) (2sqrt2M)/d^3`