The ball bearing's potential can be calculated using the charge of electrons and the radius of the ball bearing, applying the formula for the potential of a spherical conductor.
The electric potential (also known as electric potential energy per unit charge) of a 1.20 mm-diameter ball bearing with 1.60×109 excess electrons can be calculated using the formula for a spherical conductor's potential.
To calculate the ball bearing's potential, we need to know the fundamental charge of an electron and the formula for the potential of a spherical conductor, which is V = kQ/r, where V is the potential, k is Coulomb's constant (8.99×109 N·m2/C2), Q is the total charge, and r is the radius of the sphere. The charge Q can be found by multiplying the number of excess electrons by the fundamental charge of an electron (approximately 1.60×10−19 C). The radius of the ball bearing must be converted to meters to match the other units. After finding the total charge and using the given radius, the ball bearing's potential can be determined. This potential represents the electric potential energy per unit charge at the surface of the ball bearing due to the excess electrons.