Question

In which orientation of magnetic dipole its p.E is maximum?

Answer 1

Answer:

when angle between dipole and magnetic field is 180° or π

To put it in simple words, 'when they are in mutually opposite direction'

Explanation:

we know that

U=potential energy

U=MB(cosx₁-cosx₂)

where

M=magnetic dipole moment

B=applied magnetic field

x₁=angle between M and B in initial orientation

x₂=angle between M and B in final orientation

Let x₁=π/2 for our convenience of reference frame for potential energy.

Then

U=-MBcosx₂

For U to be maximum, you can:

1. differentiate the equation to get the the value of x₂ for maximum U
2. apply logic and basic reasoning

We will do it by the 2nd method as its a lot more easier and saves time

• For U to be maximum the whole quantity on RHS should be positive
• For RHS to be positive cosx₂ should be negative
• Also the maximum value of cosx₂ can be one therefore we can say that cosx₂=-1

x₂=180° or π

Therefore when x₂=π we get maximum U

x₂=π actually means that M and B are antiparallel ie they are in opposite directions to each other.

Hope this helps.