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## Homework Statement

How much work must be done to carry a +2.3 X 10^-3 C charge from 65 cm to 15 cm?

From the question:

q=+2.3 X 10^-3 C

r1= 65 cm = 0.65 m (these must be converted to metres)

r2= 15 cm = 0.15 m

k= 9.0 X 10^9 Nm^2/C^2

W=?

W=∆Ee

∆Ee=q∆V

(I'd just like to say that this question is from grade 12 physics)

## Homework Equations

Ok here’s the formulas i've been given.

Fe=Kq1q2/r^2

E=kq/r^2

E=Fe/q

Ee=Kq1q2/r

∆Ee=Kq1q2(1/r2 - 1/r1)

∆Ee=q∆V

V=Kq/r

V=Ee/q

E=∆V/r

W=∆Ee=q∆V

q=Ne

Where K is coulombs constant (I think that’s what it’s called) K=9.0 X 10^9 Nm^2/C^2

I hope the people who try to help know what those formulas are already. If not I can tell you what they are.

## The Attempt at a Solution

From the question:

q=+2.3 X 10^-3 C

r1= 65 cm = 0.65 m (these must be converted to metres)

r2= 15 cm = 0.15 m

k= 9.0 X 10^9 Nm^2/C^2

W=?

W=∆Ee

∆Ee=q∆V

So I thought ok, so I need to find ∆V now. Rearranging ∆Ee=q∆V for ∆V.

∆V=∆Ee/q

What equations have ∆V in them?

∆Ee=q∆V (well we are trying to find ∆Ee already)

E=∆V/r (oh so I need to find E now)

What equations have E in them?

E=kq/r^2 (can't use this equation thought because there is two radius's, r1 and r2, and this equation only has one.

E=Fe/q (oh so now i need to find Fe)

What equations have Fe in them?

Fe=Kq1q2/r^2 (but I can’t use that equation because I only have one q)

E=Fe/q (can’t use this equation either because I was trying to find Fe to find E from the other equation)

Then I thought wait there’s also the equation ∆Ee=Kq1q2(1/r2 - 1/r1), but again the question only gives one q. I could only use this equation if q=q1 and q2=q1, but I cannot be sure of that.

It’s like a circle that brings me to nowhere so I am stumped.

Someone from another website told me this:

"As long as you move the charge in a space where no electric field is detected the work is equal to zero. in order to give your problem a physical meaning you should precise the electric field in which the charge moves, which could be generated by another point-like charge or an uniform electric field."

The problem is the question gives no other point charge, so I don't know what to do. I am stuck at this point. If you can help I would greatly appreciate it. This question is from a "take home quiz" from my grade 12 physics class. It is due on Monday April 28, 2008, 3 days from today, so if anyone could help sooner than later would be better. Thanks.