Scaling problem with potential difference change and calculation of original length

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

SammyS

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

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

Thank you guys.
I did it like this with your help.
Is this mathematicaly sound.
Thanks
Mr C

SammyS

That answer is correct.

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