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

jackster18

## 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.

Mentor
missing information

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."
That's the same comment I would make. In order to find the work done, you need to know what force acts on the charge. Did you present the problem exactly as it was given to you, word for word? Does it refer to a previous problem or other information?

jackster18
Here’s the entire question, yes there is two parts, but it doesn’t make sense to me why you would use this from the other question.

1.a) What is the electric potential from a charge of 3.0 X 10^-5 C at 15 cm and 65 cm?
b) How much work must be done to carry a +2.3 X 10^-3 C charge from 65 cm to 15 cm?

a) q= 3.0 X 10^-5 C
r= 15 cm = 0.15 m
k = 9.0 X 10^9 Nm^2/C^2
V=?
V=kq/r
V=((9.0 X 10^9 Nm^2/C^2)(3.0 X 10^-5 C))/0.15 m
V= 1800000 V
V= 1.8 X 10^6 V

Same for the second part except r= 65 cm = 0.65 m
We find that V= 415384.62 V which is 4.2 X 10^5 V.

NOWHERE on the sheet does it say to use the charge 3.0 X 10^-5 C from question a) in question b) but I cannot see any other way to do the question unless I do use that, unless you now know what to do from this new information.

jackster18
That is exactly what it says on the sheet for the questions.

Mentor
This is a two part question. Of course you're supposed to use the information in part a to do part b! Part b is meaningless without the background of part a. In fact you use the result of part a to do part b.

Hint: If you know the meaning of the electric potential calculated in part a, part b should be a snap.

jackster18
ok so from a) the part where the radius is 0.15,I got v=1.8 X 10^6 V, when the radius is 0.65 m i got V= 4.2 X 10^5 V...

so i guess...∆V=V2-V1...and in part b r1=0.65 m (where v1= 4.2 X 10^5 V) and r2=0.15 m (where v2= 1.8 X 10^6 V)...so i just go:

∆V=V2-V1
=1.8 X 10^6 V - 4.2 X 10^5 V
= 1380000 V

∆V = 1380000 V
q=+2.3 X 10^-3 C
Using the equation ∆Ee=q∆V

∆Ee=q∆V
=(+2.3 X 10^-3 C)(1380000 V)
=3174 J

or do i do it this way?:

From a) q1=3.0 X 10^-5 C, from b) q2=+2.3 X 10^-3 C

Using the equation ∆Ee=Kq1q2(1/r2 - 1/r1)

∆Ee=Kq1q2(1/r2 - 1/r1)
=(9.0 X 10^9 Nm^2/C^2)(3.0 X 10^-5 C)(+2.3 X 10^-3 C)(1/0.15 cm -1/0.65 m)
=3184.62 J

Hmm...the answers are almost the same but not exactly...any thoughts?...maybe rounding error

jackster18
yes, it is just rounding error, i used the exact value of V1= 415384.62 V and got the answer 3184.62 V, thanks for helping :)

jackster18
I guess doing it this way:

"Using the equation ∆Ee=Kq1q2(1/r2 - 1/r1)

∆Ee=Kq1q2(1/r2 - 1/r1)
=(9.0 X 10^9 Nm^2/C^2)(3.0 X 10^-5 C)(+2.3 X 10^-3 C)(1/0.15 cm -1/0.65 m)
=3184.62 J"

is better because i am not using numbers that i calculated from before which could create errors.

Mentor
Those two methods are identical. (Compare the equations!) The answers match to 2 significant figures.

The only reason the answer are different at all is rounding error. Redo the calculations without rounding anything off until the last step. (Don't round off the potentials in part a.)

jackster18
im not smart enough to see that each way is identical, i guess by looking at the units and cancelling them out?

jackster18
oh u mean by two significant figures the "31" part of the number?

jackster18
Thanks again for help.

Mentor
im not smart enough to see that each way is identical, i guess by looking at the units and cancelling them out?
Sure you're smart enough!

From part a, you have:
V=kq/r
So:
∆V=Kq1(1/r2 - 1/r1)
And thus:
W = ∆Vq2 = Kq1(1/r2 - 1/r1)q2

Which is identical to what you did for the second method.
oh u mean by two significant figures the "31" part of the number?
Yes. (Although it would round off to "32".)
Thanks again for help.
You are welcome!