Question

Two short magnets (1) and (2) of magnetic moments `2Am^2` and `5Am^2` respectively are placed along two lines drawn at `90^@` to each other as shown in figure. At the point of intersection of their axes, the magnitude of magnetic field is `nxx10^-5T`. What is n?

Answer 1

Correct Answer - `(2)`
Here, `M_1=2Am^2`, `d_1=0*3m`
`M_2=5Am^2`, `d_2=0*4m`
The point of intersection P lies on axial line of the two magnets, figure.
`:. B_1=(mu_0)/(4pi)xx(2M_1)/(d_1^3)=10^-7xx(2xx2)/((0*3)^3)`
`=1*48xx10^-5T` along `S_1N_1`
`B_2=(mu_0)/(4pi)xx(2M_2)/(d_2^3)=10^-7xx(2xx5)/((0*4)^3)`
`=1*56xx10^-5T` along `S_2N_2`
As `B_1` and `B_2` are perpendicular to each other, therefore resultant magnetic field at P is
`B=sqrt(B_1^2+B_2^2)`
`=sqrt((1*48xx10^-5)^2+(1*56xx10^-5)^2)`
`=2*15xx10^-5T=nxx10^-5T`
where `n=2*15`, which can be taken as 2