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Scaling problem with potential difference change and calculation of original length

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mrcotton
#1
Jan8-13, 05:05 PM
P: 120
The electric potential at a distance r from a positive point charge is 45V. The potential
increases to 50 V when the distance from the charge decreases by 1.5 m. What is the
value of r?

A 1.3m
B 1.5m
C 7.9m
D 15m
1. The problem statement, all variables and given/known data

the answer is D

2. Relevant equations
V=(1/4∏ε) q/r
v proportional to 1/r

3. The attempt at a solution
5=(q/(1/4∏ε))*((1/r-1.5)-(1/r))

How embarrassing I just canít get my head around this one. Am I setting the equation up correct to solve.
If I have I need desperate help with the algebra.
Thank you
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SammyS
#2
Jan8-13, 05:16 PM
Emeritus
Sci Advisor
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PF Gold
P: 7,819
Quote Quote by mrcotton View Post
The electric potential at a distance r from a positive point charge is 45V. The potential
increases to 50 V when the distance from the charge decreases by 1.5 m. What is the
value of r?

A 1.3m
B 1.5m
C 7.9m
D 15m
1. The problem statement, all variables and given/known data

the answer is D

2. Relevant equations
V=(1/4∏ε) q/r
v proportional to 1/r

3. The attempt at a solution
5=(q/(1/4∏ε))*((1/r-1.5)-(1/r))

How embarrassing I just canít get my head around this one. Am I setting the equation up correct to solve.
If I have I need desperate help with the algebra.
Thank you
You have one equation and two unknowns.

Taking the ratio [itex]\displaystyle \ \ \frac{V(r)}{V(r-1.5)}\ \ [/itex] might be more helpful.

Otherwise, use your equation along with [itex]\displaystyle \ \ V(r)=45=\frac{q}{4\pi\epsilon_0\,r}\ \ [/itex] then eliminate q & solve for r.
gneill
#3
Jan8-13, 05:21 PM
Mentor
P: 11,867
You're going to want to get rid of the constants you don't have values for (like the charge value q) so you'll probably want to set it up as a ratio so that they'll cancel out.

EDIT: SammyS got their first!

mrcotton
#4
Jan8-13, 05:36 PM
P: 120
Scaling problem with potential difference change and calculation of original length

Thank you guys.
I did it like this with your help.
Is this mathematicaly sound.
Thanks
Mr C
SammyS
#5
Jan8-13, 10:40 PM
Emeritus
Sci Advisor
HW Helper
PF Gold
P: 7,819
Quote Quote by mrcotton View Post
Thank you guys.
I did it like this with your help.
Is this mathematically sound.
Thanks
Mr C
That answer is correct.
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