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Question
Show that the magnetic field at a point due to a magnetic dipole is perpendicular to the magnetic axis if the line joining the point with the centre of the dipole makes an angle of `tan^-1(sqrt 2)` with the magnetic axis
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Solution
Given :
Angle made by observation point P with the axis of the dipole, `θ = tan^-1 (sqrt 2)`
⇒ `tan θ = sqrt 2`
⇒ `2 = tan^2 θ`
⇒ `tan θ = cot θ`
⇒ `tan θ /2 = cot θ` .....(1)
we know ,
`tan θ /2 = tan α` ....(2)
On comparing (1) and (2), we get
`tan α = cot θ`
⇒ `tan α = tan (90 - θ)`
⇒ `α = 90 - θ`
⇒ `θ + α = 90^circ`
Hence, the magnetic field due to the dipole is perpendicular to the magnetic axis.
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