# Scaling problem with potential difference change and calculation of original length

by mrcotton
Tags: calculation, difference, length, original, potential, scaling
 P: 107 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 can’t 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
Emeritus
HW Helper
PF Gold
P: 7,398
 Quote by mrcotton 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 can’t 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 $\displaystyle \ \ \frac{V(r)}{V(r-1.5)}\ \$ might be more helpful.

Otherwise, use your equation along with $\displaystyle \ \ V(r)=45=\frac{q}{4\pi\epsilon_0\,r}\ \$ then eliminate q & solve for r.
 Mentor P: 11,417 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!
P: 107

## 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
Emeritus