Question

Two identical bar magnets each of magnetic moment M, separated by some distance are kept perpendicular to each other. The magnetic induction at a point at the same distance d from the centre of magnets, is (µ₀ = permeability of free space)

विकल्प

• `µ_0/(4π) (sqrt3) "M"/"d"^3`

• `µ_0/(4π) (sqrt2) "M"/"d"^3`

• `µ_0/(4π) (sqrt5) "M"/"d"^3`

• `((2µ_0)/π) "M"/"d"^3`

Answer 1

`µ_0/(4π) (sqrt5) "M"/"d"^3`

Explanation:

The situation is as shown below

The magnetic field at P due to first magnet is

B₁ = `(µ_0)/(4π) xx (2"M"_1)/"d"^3` ......(along M₁)

and magnetic field at P due to second magnet is

B₂ = `(µ_0)/(4π) xx ("M"_2)/"d"^3` ......(opposite to M₂)

The resultant field at P,

B = `sqrt("B"_1^2 + "B"^2_2) = µ_0/(4π"d"^3) sqrt(4"M"_1^2 + "M"_2^2)`

= `µ_0/(4π) (sqrt5) "M"/"d"^3` ....(∵ M₁ = M₂ = M)