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Find the magnetic field due to a dipole...

Find the magnetic field due to a dipole of magnetic moment `3Am^(2)` at a point 5m away from it in the direction making angle of `45^(@)` with the dipole exists

A

`3.79xx10^(-9)T` , `alpha=tan^(-1)(1)`

B

`3.79xx10^(-9)T` , `alpha=tan^(-1)(0.5)`

C

`3.79xx10^(-8)T` , `alpha=tan^(-1)(0.5)`

D

`3.79xx10^(-6)T` , `alpha=tan^(-1)(1)`

Text Solution

Verified by Experts

The correct Answer is:
B

So, the magnetic field at point P is,
`" " B=(mu_(0))/(4pi)(M)/(r^(3)) sqrt(1+3 cos^(2)theta)`
`Here, M=3 Am^(2),r=5m, theta=45^(@)`
`therefore " " B=10^(-7)xx(3)/((5)^(3)) sqrt(1+3 cos^(2)(45^(@)))`
`therefore " " =10^(-7)xx(3)/(125) xx1.58=3.79xx10^(-9)T`
`Also, tan alpha =(1)/(2) tan theta=(1)/(2)tan45^(@)=(1)/(2) Rightarrow alpha=tan^(-1)(0.5)`
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