Example: Electric Potential from a Positively Charged Balloon
Suppose we have a positively charged balloon with total charge Q=5.0⋅10−9 C. What is the electric potential (also called voltage) at a point P, which is a distance R=50 cm from the center of the balloon?
Facts
- The balloon has total charge Q=5.0⋅10−9 C.
- The point P is a distance R=50 cm away from the center of the balloon.
- The electric potential due to a point charge can be written as V=14πϵ0qr,where q represents the charge and r is the distance.
Representations
Assumption
We assume P lies outside of the balloon. We make this assumption because it was not specified, but this seems to make more sense than P being inside the balloon. This also helps us draw the representation below, which can be used to bolster our approximation later on of the balloon as a point charge.
Goal
- Find the electric potential at P.
Solution
Approximation
We approximate the balloon as a point charge. We do this because we have the tools to find the electric potential from a point charge. This seems like a reasonable approximation because the balloon is not too spread out, and we are interested in points outside the balloon. so the balloon might “look” like a point charge from the perspective of an observation location that is little far away.
Assumption
The electric potential infinitely far away from the balloon is 0 V. Read here for why this is important.
The electric potential at P is given by V=14πϵ0qr=14π⋅8.85⋅10−12CVm5⋅10−9 C0.5 m=90 V