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- anonymous

Show that an infinite line of charge with linear charge density lamda exerts an attractive force on an electric dipole with magnitude F = (2)(Lamda)(p) / (4)(pie)(Epsilon knot)(r^2). Assume that r is much larger than the charge separation in the dipole.

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- anonymous

- schrodinger

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- anonymous

http://web.mit.edu/6.013_book/www/chapter11/11.8.html

- anonymous

What part of this is the answer?

- anonymous

I don't understand what the answer is

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- anonymous

start with the field of an infinite line of charge, what is that?

- anonymous

E= 1/(4pi€.) * ( 2(lambda))/r. Then what do I do?

- anonymous

differentiate and multiply by p :)

- anonymous

How would I differentiate? By dx?

- anonymous

did you look over the "force on a dipole" section?

- anonymous

Is the derivation clear?

- anonymous

r

- anonymous

Yes. I think. Lol

- anonymous

Do I differentiate or integrate?

- anonymous

differentiate that upside down triangle is the gradient (space derivative)

- anonymous

here everything only depends on r, no x's y's or z's needed to characterize the problem...

- anonymous

so the gradient is just the derivative with respect to r

- anonymous

Differintiating will get rid of r

- anonymous

nope. r is the variable.

- anonymous

what's the derivative of 1/r with respect to r?

- anonymous

\[-1/r ^{2}\]

- anonymous

Okay I got it. Is the final answer suppose to be negative?

- anonymous

all the rest of the terms are constants, they stay unchanged... multiply by the dipole moment (p) and you're done...

- anonymous

yes negative r hat is towards the center so it's an attractive force...

- anonymous

Oh now it makes sense thank you so much!! I may pass my quiz tomorrow now!

- anonymous

Hope it helped:) gl on the quiz!

- anonymous

Thanks

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