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15 Jan 2008 16:48:49 IST

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HCV__2 pgno.--231,Qno.13

None

a hypothetical magnetic field existing in the region is given by B=Be^,e^ is unit vector alongradial dir.

circular loop, radius a,parallel to xy plane,centre at(0,o.d).

find magnetc force acting.

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Anshuman Johri

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Joined: 27 Jan 2007

Posts: 559

15 Jan 2008 17:26:11 IST

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the situation is the one as shown in the fig...

on a small element dl force acting can be given as

dF = iBdl

=> dF= i Be^ dl

Resolving this force (shown in red) in 2 perpendicular directions the vertical components will get canceled.

so

F =

dF (Horizontal)

=

i B sin@ dl
= iB*(2 pi a)*a /sqrt(a²+d²)

=> F = (2 pi a²iB)/sqrt(a²+d²)

abhishek sinha

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Joined: 18 Dec 2007

Posts: 926

17 Jan 2008 13:41:02 IST

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It is simple !!!!!!!!!!!!

I am giving u the formal approach to solve the problem

see , dF = I dl * B

Now B = B er

& dl = dl e ( Where er ,e& e are the unit vectors in the spherical coordinate )

Taking the cross product , we have dF = I B e dl

( because e * er = e )

Now e = cos

cos

i + cos

sin

j - sin

& dl = a d

Integrating dF , (

limiting from 0 to 2

) noting that i & j component cancels ,

We have F = 2

BIa sin

Now sin

= a / sqrt ( a^2 + d^2 )

so Force = F = 2

BI a^2 / sqrt ( a^2 + d^2 ) k

abhishek sinha

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Joined: 18 Dec 2007

Posts: 926

18 Jan 2008 20:53:00 IST

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But I should warn you that this is not a physical problem , only a mathematical exercise .

Because , according to Maxwell's eqn we must have

div B = 0

But for B = B er we have div B = 2 B / r which is non zero everywhere .

So nowhere in our universe you can find such a magnetic - field distribution.

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