Magnetic field strength and SHM

[debwaldy]

Homework Statement

Hi there.this is one of those proof dealies that i think i nearly have right but i was wondering if anyone could point out if i have made too many assumptions or anything thanks.
Show that if a bar magnet is suspended in a uniform magnetic field, of strength H, and is displaced slightly from equilibrium, it undergoes SHM with period:
T = 2*pi* (I/plH)^1/2, where I is the moment of inertia, p is the magnetic pole strength, and l is the separation between the poles of the bar magnet.

Homework Equations

T= pln X H
P= 2*pi*(I/plH)^1/2

The Attempt at a Solution

I said: Torque on magnet T=pln X h
T(alpha) = -plhsin(alpha) =-plH * alpha which is proportional to - alpha => SHM

T/alpha = plH

P= 2*pi* (moment of inertia about axis of rotation/restoring torque per unit angular displacement)^1/2
=> P = 2*pi*(I/plH)^1/2
Q.E.D?

 

[debwaldy]

will i take it as being Q.E.D'd then ya?

 

[m2003]

I would first commend the student for their attempt at a solution and for recognizing the importance of proving their assumptions. However, I would suggest that they clarify their equations and provide more detailed explanations for each step. For example, they could explain why the torque on the magnet is proportional to the angular displacement and how this leads to SHM. Additionally, they could provide a diagram or illustration to help visualize the situation. It would also be helpful to define any variables that may not be familiar to the reader, such as the moment of inertia and magnetic pole strength. Overall, the student has the right idea and with some further clarification, their proof could be more convincing.