## haganmc 3 years ago 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.

1. Algebraic!
2. haganmc

What part of this is the answer?

3. haganmc

I don't understand what the answer is

4. Algebraic!

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

5. haganmc

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

6. Algebraic!

differentiate and multiply by p :)

7. haganmc

How would I differentiate? By dx?

8. Algebraic!

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

9. Algebraic!

Is the derivation clear?

10. Algebraic!

r

11. haganmc

Yes. I think. Lol

12. haganmc

Do I differentiate or integrate?

13. Algebraic!

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

14. Algebraic!

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

15. Algebraic!

so the gradient is just the derivative with respect to r

16. haganmc

Differintiating will get rid of r

17. Algebraic!

nope. r is the variable.

18. Algebraic!

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

19. Algebraic!

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

20. haganmc

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

21. Algebraic!

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

22. Algebraic!

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

23. haganmc

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

24. Algebraic!

Hope it helped:) gl on the quiz!

25. haganmc

Thanks