Electric Potential Energy Electrostatics Electric Potential Energy

Objectives Define electric potential energy and change in electric potential energy Solve 2 point charge problems at rest involving: Electric potential energy Charge Distance of separation Moving 2 point charge problems involving: Change in electric potential energy Distance of separation (initial and final)

Electrical Potential Energy Recall equation for electrical force: FE = kQ1Q2/r² When we were looking at gravitational forces, how did we find work done? Area under the graph. FE r

Electrical Potential Energy FE r Recall that potential energy is zero at infinity ∞

Electrical Potential Energy EP = kQ1Q2/r When using the potential energy equation, keep the following in mind: Amount of potential energy due to separation of two charged particles by distance “r”. Include the signs of the charged particles Drop the - sign

Electrical Potential Energy EP = kQ1Q2/r Drop the - sign, you’ll see! A + particle has its highest energy when close to another + particle A - particle has its highest energy when far from a + particle Oppositely charged particles have low energy when they are close together At ∞ Highest Energy ie. 0J Lowest Energy ie. -100J Some Energy ie. -50J + Q1 - - - Q2 Q2 Q2 + + + Highest Energy ie. 100J Some Energy ie. 50J At ∞ Lowest Energy, ie. 0J

Electrical Potential Energy Ex 1 How much potential energy does a 1mC charge have when it is 1m away from a 5C charge? EP = kQ1Q2/r EP = (9x109Nm²/C²)(5C)(0.001C)/(1m) EP = 4.5x107J Relative to zero at infinity 5C 1mC 1m

Electrical Potential Energy Ex 2 Same 2 particles, how much work is necessary to move the 1mC charge to 1.5m away? W = ΔEP = EPf - EPi W = kQ1Q2/rf - kQ1Q2/ri W = kQ1Q2[1/rf - 1/ri] W = (9x109)(5)(0.001)[1/(1.5m) - 1/(1m)] W = -1.5x107J -, so work has been done by charges (energy & work are not vectors) 1mC 1mC 5C 1.5m

Conclusions Potential Energy: EP = kQ1Q2/r Like charges experience a + potential energy that increase the closer they are together Opposite charges experience a - potential energy that decreases the closer they are together Particles experience zero potential energy when they are infinitely far apart from one another

Electric Potential Voltage Electrostatics Electric Potential Voltage

Electrical Potential We have already looked at the amount of energy a charge has: E = kQ1Q2/r But that is rarely useful, let’s look at the total amount of energy a charge has: ELECTRIC POTENTIAL

Alessandro Volta - Built the first battery Electrical Potential Electric Potential is also sometimes called just simply “Potential” Symbol is “V” (Named after Volta) Measured in Volts (J/C) It is the amount of work required to move a unit of charge from point A to point B V = EP/q V = (kQq/r) / q V = kQ/r Alessandro Volta - Built the first battery

Electrical Potential Example: Find potential of the -5mC charge at 1.5m and at 5m away? V = kQ/r V1.5 = (9x109J)(-0.005C)/(1.5m) V1.5 = -3x107V V5 = (9x109J)(-0.005C)/(5m) V5 = -9x106V -5mC V1.5 1.5m 5m V5

Electrical Potential Example Cont’d: What is the potential difference between 1.5m and 5m? ΔV = V5 - V1.5 ΔV = (-9x106V) - (-3x107V) ΔV = 2.1x107V ΔV -5mC V1.5 V5 1.5m 5m

Work required to move a charge from one voltage to another Electrical Potential From the previous example, consider the following: ΔV = Vf - Vi ΔV = EPf/q - EPi/q ΔV = (EPf - EPi)/q ΔV = W/q W = ΔV*q Work required to move a charge from one voltage to another

Electrical Potential Example Cont’d: How much work does it take to move a 1μC charge from 1.5m to 5m? W = ΔV*q W = (2.1x107V)(1x10-6C) W = 21 J 1μC 1μC 1μC -5mC V1.5 V5 1.5m 5m

Conclusions Electric Potential, Potential, Voltage Same Diff Measured in Volts V = kQ/r W = ΔV*q Zero volts is sometimes called ground Symbol is