Find the electric potential negligibly far outside a 23.0-centimeter-diameter metal sphere that has a net positive charge of 3.4 microcoulombs.
Since our sphere is made of metal, which will allow the charge on it to move easily, we can assume that the charge on the sphere is evenly distributed across its surface. Under that assumption and since we’re calculating the electric potential outside the sphere, we can model all this charge as though we’re at the very centre of the sphere collected in a one point.
In a sense then, it’s as though we’re calculating the electric potential a certain distance away from a point charge of 3.4 microcoulombs. The electric potential created by a point charge is equal to Coulomb’s constant 𝑘 times the charge itself 𝑄 divided by the distance from that point charge to where we want to solve for the potential.
In our case, since we’re solving for electric potential negligibly far outside the sphere, we can effectively put a point on the surface of the sphere and solve for the potential there. That means our radius 𝑟 will simply be the radius of our metal sphere.
That radius is half of the diameter, in other words, 11.5 centimeters. And the charge 𝑄 we’re told is 3.4 times 10 to the negative six coulombs. When we look up the value for 𝑘, Coulomb’s constant, we find its approximately equal to 8.99 times 10 to the ninth newton metres per coulomb squared.
When we plug in these three values, being careful to convert our radial distance into units of metres, and enter this expression on our calculator, to two significant figures, we find that 𝑣 is 270 kilovolts. That’s the electric potential created just outside the sphere.