Question

charged particles each of magnitude \(2.00 \mu C\) are located on the x axis, one is at x=1.00m, the other is at x=-1.00m.

Determine the electric potential on the y axis at y=0.500m.

Answer 1

I don't understand why this is zero. why is it zero?

Answer 2

Im not sure either. I would expect it to be zero if this were the case

hope you find out

Answer 3

I'm pretty sure it's not zero and my book has the wrong answer. All I did was say \[V=\frac{1}{4\pi\epsilon_0}\sum^i_{i=1}\frac{q_i}{r_i}\]\[V=\frac{2q_1}{4\pi\epsilon_0r_1}\]Since \(r_1=r_2\) and \(q_1=q_2\)

Is this correct?

Answer 4

horizontal components cancel leaving vertical\[\vec E=\frac{2q}{4\pi\epsilon_0r^2}\sin\theta\hat j=\frac{2qy}{4\pi\epsilon_0r^3}\hat j\]bringing a point charge along y from +infty\[V=\int_{\infty}^{1/2}Edy=\frac q{2\pi\epsilon_0}\int_\infty^{1/2}\frac y{(1+y^2)^{3/2}}dy\]\[=\frac q{2\pi\epsilon_0\sqrt{1+\frac14}}=\frac {q_0}{\pi\epsilon\sqrt5}\]a nice answer, but not zero
I agree your book is wrong

Answer 5

slight typo\[=\frac q{2\pi\epsilon_0\sqrt{1+\frac14}}=\frac q{\pi\epsilon_0\sqrt5}\]

Answer 6

@turingtest
That's the right answer. You don't need to go through all that however,
it's simply 2kq/r where r= sqrt(5/4)

Answer 7

lol I know, I just wanted to be rigorous. I always feel better about disagreeing with the book when I can prove something from scratch.

Answer 8

thanks, you think paying $250 for a textbook and two solution manuals they could put some effort into explaining solutions (or at least give correct answers!) haha.