Goal: To understand electric potential and electric potential energy Objectives: To compare Electric potential energy to gravitational potential energy. To Compare Electric Potential to Electric force. To learn how to Find the Electric Potential energy. To understand the similarities and differences between Voltage and energy To learn about Equipotential surfaces To understand how to find the electric Potential in a Uniform Electric Field
Revisit of Gravitational Potential Energy • Potential energy is the energy you can get from letting something move. • For gravity if you drop something you can convert Potential Energy to Kinetic. • The energy you get is approximately the force times the distance (yes that is similar to work).
Electric Potential Energy • Electric Potential energy is the same. It is the potential energy between any two charges. • Energy is a force times a distance, so if you multiply the Electric Force times a distance (I am oversimplifying a little here) you get the Electric Potential. • U = k q1 q2 / r (and is in units of Joules) • Note how similar it looks to the equation for the force.
Sample problem • Calculate the electric potential energy between the following 2 charges: • Q1 = 5C, and is located at x = 3 m, Q2 = -3C, and is located at x = -2 m.
Negative energy? • The negative because it is attractive. Therefore it TAKES energy to separate them. • If the energy is positive then you gain energy by separating them. • The energy is defined to be the energy you get if you send them to infinity (or need to add if negative).
Follow up! • Q1 = 5C, and is located at x = 3 m, Q2 = -3C, and is located at x = -2 m. • Three follow up questions: • Suppose we started these charges at rest at infinity. When they were at infinity what was: • A) The potential Energy • B) The total energy (hint how much is the kinetic if they are at rest?)
Follow up! Part two • Q1 = 5C, and is located at x = 3 m, Q2 = -3C, and is located at x = -2 m. • Three follow up questions: • Suppose we started these charges at rest at infinity. Now we let them go until they reach the position above • A) What is the total energy when they reach their locations? • B) How much Kinetic Energy will they have?
Okay now for a bit harder • Suppose there are > 2 charges! • The total potential energy is the sums of the potentials for each pair. • So, if you have 3 charges then: • U = U13 + U12 + U23 • Where Uab = k qa qb / r (r = distance between a and b) • Be careful not to add in a pair twice.
3 charges in 1 dimension • Calculate the total potential energy. • Q1 = 4C, and is at x = -3 m • Q2 = -3C, and is at x = 1 m • Q3 = 2C, and is at x = 4 m
Charges in 2D • Think about charges in 2 dimensions. • Other than calculating distances between charges will the directions matter? • Why or why not?
Electric Potential • Not to be confused with Potential energy. • This is the potential energy per unit charge. • The units of potential is Volts (V) • V = U / q or U = q * V • Notice that a Volt = 1 J / 1 C
Sample • A 3 C charge is allowed to move across a 5 V potential. By how much has the potential energy changed (asking for a magnitude here)?
Equipotential surfaces • Equipotential surfaces are surfaces with equal potentials. • They are perpendicular to the electric field lines. • This is like a line on a map where everything on that line is at the same elevation (thus same gravitational potential). • Why would this be important?
Uses for surfaces • Along the equipotential surface no net work is required! • If you go perpendicular to a surface then you maximize your increase or decrease in potential.
Potential in a Uniform Electric Field • Work is energy. • Work = Force * distance • Since Force = q * E, if E is constant, then W = q * E * d • The change in potential energy is just the negative of the work done, so U = - qEd
Potential in a Uniform Electric Field • Since V = U / q, therefore V = - E d • Warning: Don’t mix up V, E, and U. • V is voltage (electric potential), E is electric field, and U is potential energy. Note V and U are different even though both have ‘potential’ in them. • Students often times find energy with E = -V/d, but that isn’t energy…
Quick sample if time permits • A charge of 5C is located inside a constant electric field of 7 V/m. • What is the change in potential for the charge if the charge move 3 m. • What is the change in potential energy for the charge (no it won’t be the same answer as for A)? C) If the charge was initially at rest how much kinetic energy will it have after it travels 3 m (hint: how does change in kinetic energy depend on the change in potential energy?)? D) If the mass of the charge is 1 kg then at what velocity will it be traveling after it travels 3 m?
Conclusion • We have found that potential energy and voltages are scalars. • We found that U = k q1 q2 / r for any pair of charges. • For multiple charges U is just the sums of U for each possible pair. • Voltage is just a energy per charge so V = U/q. • Equipotential surfaces are perpendicular to field lines. • In a uniform field W = qEd and V = -Ed