Question

Two long, thin electrified wires intersect the plane of the paper normally at points A and B. The magnitude of E-field due to each wire is 1/r (N/m), its direction being radially away from the wire. Find the potential difference between points C and D. (CD is a perpendicular bisector to AB). Take AC = CB = 4.00m, CD = 10.12 m and AD = 10.88m.

http://www.wellesley.edu/Physics/phyllisflemingphysics/108_p_potential_images/figure_for10.gif

Answer 1

Original Idea here was to find Voltage between Infinity and D, and either A or B and C, then take a difference of the voltage at C and D. Having trouble solving for voltage at C using this method.

Answer 2

Are you comfortable calculating the voltage bringing a test particle from infinity away to a distance r away from either of the thin wires? (Pretend there is only one wire)

Answer 3

Not so much so, we end up with the natural log of infinity minus the natural log of r, no?

Answer 4

Oh yeah sorry. That says it takes an unbounded amount of work to push the test particle from infinity toward the wire. This makes sense I guess. Unlike the case of pushing a test particle toward a small point charge, the repulsive force from the wire is much more "felt/noticeable" by a test particle at large distances.

Answer 5

So you did the integral and you get a difference between natural logs for the initial and final distances to the wire of interest right?

Answer 6

While in lecture one of those "positions" is often chosen to be a reference point at infinity, we are free to calculate the work to move a test charge particle between any two points that we find interesting.

Answer 7

Right, we know the voltage at infinity has to be 0, so it's a nice reference point, but in the case of the integral, and voltage difference, it doesn't work out so niftily.

Answer 8

Actually the voltage at infinity is not necessarily zero. That's just a convention.

Answer 9

Ah, I still think the convention applies to this case, no?

Answer 10

An absolute voltage is not really physical. Only voltage differences are physical. ... but we can get back to the HW problem. (I'm trying not to give the answer directly if that's ok).

Answer 11

So if I were to ask you to calculate the voltage difference between *finite* positions at Rf and Ri away from a wire, you could do it.

Answer 12

That would be fine, right? No weird business with infinity messing things up.

Answer 13

indeed! So long as Rf and Ri are within the domain of ln. IE not <= 0

Answer 14

How far is point C from the wire centered at A? :)

Answer 15

Ohhh, the wires are in the z-hat direction, aren't they?

Answer 16

Yes!

Answer 17

Haha, ah, see that would help!

Answer 18

(or the "out of the page" direction)

Answer 19

Doh! Alright, let me work this out for a few minutes, thanks!

Answer 20

I probably won't look back b/c I think other than what we just chatted about the rest is making sure negative signs and units show in the right place. And honestly that's boring. :)

Answer 21

(but if any college or tutoring company is looking at this, I didn't just say that :)

Answer 22

xD, no problemo and thank you again!

Answer 23

Welcome :)