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Magnetism

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 Joined: 4 Jan 2009 Post: 8
5 Jan 2009 19:49:54 IST
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Engineering Entrance , Medical Entrance , AIPMT , JEE Main , AIIMS , JEE Advanced , Physics , Magnetism

I am unable to obtain the function that must be integrated in order to get the final expression. Please help.

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Joined: 19 Aug 2008
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6 Jan 2009 18:42:41 IST
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Hi
Kindly post complete question, for fast replies

~moderator

New kid on the Block

Joined: 4 Jan 2009
Posts: 8
7 Jan 2009 00:45:53 IST
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The question is:

Consider a solid sphere of radius 'r' and mass 'm' which has a charge 'q' distributed uniformly over its volume. The sphere is rotated about a diameter with an angular speed 'ω'. Show that the magnetic moment 'μ', and the angular momentum 'l' of the sphere are related as :

μ = ql / 2m

Blazing goIITian

Joined: 20 Dec 2008
Posts: 599
7 Jan 2009 14:41:25 IST
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Let the sphere's centre be at the origin and it be rotating about the z axis.

So angular momentum = [ Assuming that it rotates counter clockwise as seen from above ]

Let there be a disk whose z coordinate is a and thickness da.

Let there be a ring of radius x on this disk and thickness dx.

Area of ring = .

Volume of ring = 2 x dx da.

Charge on ring = 2 x dx da / (4/3 ) Q = .

As time period of a complete revolution is 2 / , the current in this ring is / (2 / ).

Area vector of the loop of the current is   .

So of the ring is   * / (2 / )

=

Integrating the expression w.r.t. x to find of the disk and then keeping the limits 0 and ( the z coordinate of the disk is a so its radius is ), we get the of the disk as .

To get the of the sphere, we have to integrate this and put the limits -R to R (as a varies from -R to R).

Expansion of the square, integration and putting the limits leaves us with = =

Hence proved.

Blazing goIITian

Joined: 24 Dec 2007
Posts: 1111
7 Jan 2009 19:15:46 IST
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One thing I'd like to point out the following fact:

ALL SYMMETRIC SYSTEMS WITH CHARGE EVENLY SPREAD CAN BE EQUATED TO A ELECTRON ROTATING AROUNG THE NUCLEUS

Tht's wht I remember...... and this fact makes such problems very easy

current

Now magnetic moment =nIA (with n=1)

so

Now as mvr =L and area=

This reduces calculation time by a massive amount!! And mind you, this is not just a coincidence.its a proven fact.

But if you wanna do it by the integration method, 3774's method is perfect!!

hope this helps

cheers!!

Hot goIITian

Joined: 18 Dec 2008
Posts: 129
19 Jan 2009 23:01:56 IST
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hi this  the solution if u are satisfy then plase vote for it

Hot goIITian

Joined: 18 Dec 2008
Posts: 129
24 Jan 2009 18:44:45 IST
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hey tell me are you satisfy now with this mathod of intregration.............voteme mean tell me

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