Question

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.

Answer 1

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

Answer 2

What part of this is the answer?

Answer 3

I don't understand what the answer is

Answer 4

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

Answer 5

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

Answer 6

differentiate and multiply by p :)

Answer 7

How would I differentiate? By dx?

Answer 8

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

Answer 9

Is the derivation clear?

Answer 10

r

Answer 11

Yes. I think. Lol

Answer 12

Do I differentiate or integrate?

Answer 13

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

Answer 14

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

Answer 15

so the gradient is just the derivative with respect to r

Answer 16

Differintiating will get rid of r

Answer 17

nope. r is the variable.

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

Hope it helped:) gl on the quiz!

Answer 25

Thanks