Electric Potential Energy Recall, for point masses, the force of gravity and gravitational potential energy are: and For point charges, it would follow that: and

Electric Potential Energy However, how are electric fields and gravitational fields different? Unlike charges attract +q-q Like charges repel +q Therefore, electric potential energy can be positive or negative:

Electric Potential Energy How do you increase the electric potential energy for charges? UNLIKE CHARGES +q-q LIKE CHARGES +q Increase the separation between the charges. Decrease the separation between the charges. LOW potential energyHIGH potential energy LOW potential energy

Electric Potential Energy Electric potential energy is defined as zero when two charges are an infinite distance apart as The change in potential energy is the work done by the electrostatic force when moving a point charge from infinity to a distance r from another point charge. +q-q In other words, our reference “point” is infinity. r

Electric Potential Energy Electric potential energy versus separation graph 0 Unlike charges Like charges

Electric Potential All charges have the potential to store energy in their electric field. +q 1 +q 2 There is no potential energy stored until another charge is placed in the field of the first charge.

Electric Potential The electric potential is defined as the electric potential energy per unit charge. For point charges: units: volt (V) 1 V = 1 J/C

Electric Potential Potential difference is the difference in electric potential from one point to another. +q 1 A B Also referred to as “voltage” Potential difference is path independent

Electric Potential Electric potential can be positive or negative depending on the sign of the charge producing the potential. A positive charge produces a positive potential. A negative charge produces a negative potential.

Electric Potential Case 1: q 1 > 0 and q 2 < 0 + q1q1 If a negative charge (-1 C) is placed at A and then moved to B, potential energy should increase. A B - q2q2

Electric Potential Case 1: q 1 > 0 and q 2 > 0 + q1q1 If a positive charge (+1 C) is placed at A and then moved to B, potential energy should decrease. A B + q2q2

Electric Potential Case 1: q 1 < 0 and q 2 < 0 If a negative charge (-1 C) is placed at A and then moved to B, potential energy should decrease. A B - q2q2 - q1q1

Electric Potential Case 1: q 1 0 If a positive charge (+1 C) is placed at A and then moved to B, potential energy should increase. A B + q2q2 - q1q1

Electric Potential The potential difference is related to the electric field strength. A B Two points, A and B, are separated by  d and have a potential difference of: dd or

Electric Potential Recall, Ohm’s Law: Here, “V” actually refers to potential difference. Why is current proportional to voltage? V + - R I

Electric Potential Equipotential lines can be drawn around charges to indicate constant electric potential. +q 1 At every point on this line, the electric potential is the same.

Example Problem For a point charge of 5e C, determine the following: a)electric field strength 5.0 cm away from the charge b)electric potential 5.0 cm away from the charge c)electric potential energy if a -2e C charge is placed 5.0 cm from the 5e C charge d)the work required to move the -2e C charge from 5.0 cm away to 10. cm away from the 5e C charge Answers: a) 2.9x10 -6 N/Cb) 1.4x10 -7 Vc) 4.6x Jd) 2.3x N/C

Example Problem

Summary In general: For point charges: