Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12

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 - Physics

Sum

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

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.

Is there an error in this question or solution?

APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 14 Permanent Magnets
Q 6 | Page 277