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Electricity

Blazing goIITian

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7 Apr 2007 18:30:11 IST

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540

max. force

None

two particles A and B having charge Q each are placed d distance apart . Where should a particle of charge q be placed on perpendicular bisector of AB so that it experiences max. force ? Also , find its magnitude .

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un.niranjan

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Joined: 11 Dec 2006

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7 Apr 2007 20:05:10 IST

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write expression for force and maximize it

CyBorG

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Joined: 6 Jan 2007

Posts: 706

8 Apr 2007 09:29:20 IST

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Let the charge q be placed at a distance x along the perpendicular bisector.

The force acting on it due to one charge Q is

F=(1/4piE₀)Qq/(x²+(d²/4))

The force due to other Q is also same.

Now resolve this into two components FsinQ and FcosQ.

Now sinQ=x/root(x²+(d²/4))

The component FcosQ will get cancelled.

So net force acting will be=2FsinQ.......... (1)

=2(1/4piE₀)Qqx/(x²+(d²/4))^3/2

For maximum differentiate this and equate it to zero.

You will get x=d/2root2

Substitute this value in (1) you will get the maximum force.

Umang

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9 Apr 2007 21:37:46 IST

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Hey adarsh !

Thanks for the solution . I am a bit hesitant to differentiation , so if u could suggest some alternative method !

Thanks !!!

rohan sen sharma

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Joined: 3 Feb 2007

Posts: 50

12 Apr 2007 22:04:28 IST

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hey if u want the differentiation part just tell me.i think there is no other way to solve it.

sorry.

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