Question

The electric field in a region is directed outward and is proportional to the distance r from the origin. Taking the electric potential at the origin to be zero, the electric potential at a distance r?

• A. Is uniform in the region
• B. Is proportional to r
• C. Is proportional to $r^2$
• D. Increases as one goes away from the origin

Answer 1

Answer: (C)

Is proportional to $r^2$

$E\propto randV=0atr=0$

$E=kr$

$E=\frac{-dv}{dr}$

$V=-intEdr$

$V=-intKrdr$

$V=-k\frac{r^2}{2}+C$

$V=-k\frac{r^2}{2}$

$V=0r=0C=0$

$V=0r=0C=0$

v is proportional to $r^2$