1. Day 15: Electric Potential due to Point Charges The Electric Potential of a Point Charge Work done to bring two point charges together The Electric Potential at an arbitrary point, due to two point charges

2. The Electric Potential of a Point Charge The Electric Field at a distance r away from a point charge Q is: The Electric Potential difference between points a and b can be derived as:

3. The Electric Potential of a Point Charge It is common to choose the potential at ∞ as zero. For r b = ∞, V b = 0 and:

4. Work Done to Bring Two Point Charges Together The work done to bring two point charges together is equivalent to the change in the potential energy of the two charges +Q q r b r a = ∞ If r a = ∞, then:

5. Electric Potential at an Arbitrary Point due to Two Point Charges To find the electric potential due to two point charges, simply take the sum of the potentials, at that point, due to each charge. r 1 P +Q 1 r 2 Q 2 Note – these are not vector quantities !