# January 30. Physics 272. Spring Prof. Philip von Doetinchem

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1 Physics 272 January 30 Spring Prof. Philip von Doetinchem Phys272 - Spring 14 - von Doetinchem - 140

2 Summary General form of Gauß's law: The total electric flux through a closed surface is equal to the total (net) electric charge inside the surface, divided by ε 0. Phys272 - Spring 14 - von Doetinchem - 141

3 Summary In electrostatics the electric field inside a solid conductor is 0, excess charges only on surface Charge in isolated cavity of neutral conductor: Excess charge in conductor can only be on the surface Phys272 - Spring 14 - von Doetinchem - 142

4 Summary Potential energy decreases if a charged particle moves in the direction of the electric field If the displacement of a positive charge is in the direction of the electric field the work is positive Phys272 - Spring 14 - von Doetinchem - 143

5 Summary Electric potential energy of two point charges: q0 moves in field of q Work only depends on radial displacement along the force does not depend on exact path, can move without loss/increase perpendicular to force Phys272 - Spring 14 - von Doetinchem - 144

6 Summary total potential energy is the algebraic sum: Phys272 - Spring 14 - von Doetinchem - 145

7 Interpreting electric potential energy Version A: Potential energy difference equals the work done by the electric force when the particle moves between two points. Version B: Potential energy difference is the work that must be done by an external force to move the particle slowly (no kinetic energy) between two points against the electric force. Different signs, be careful. Phys272 - Spring 14 - von Doetinchem - 146

8 Electric potential Describe potential energy on a per unit charge basis (like the electric field describes force per unit charge) Determination of electric field is often easier by using the potential Source: Alessandro Volta Potential energy and potential are scalars Potential difference in circuits is often called voltage Phys272 - Spring 14 - von Doetinchem - 147

9 Calculating electric potential Potential of a continuous charge distribution: Potential is zero at points that are infinitely far away from all the charges creating the potential Electric potential at a certain point is the potential energy that would be associated with a unit charge placed at that point. Phys272 - Spring 14 - von Doetinchem - 148

10 Finding electric potential from electric field If electric field is known or can be found easily: Potential does not depend on th exact path Moving with the direction of the electric field means moving in the direction of decreasing potential Moving a charge slowly against an electric field requires an external force, equal and opposite to the electric force. Phys272 - Spring 14 - von Doetinchem - 149

11 Electron volts Electric field unit: 1V/m = 1 Volt/meter = 1N/C = 1 Newton/Coulomb Useful: electron charge electron volt unit of energy For instance, very important in particle physics and to describe processes in atoms Phys272 - Spring 14 - von Doetinchem - 150

12 Benefits of electric potential Potential calculation is sometimes easier than the electric field calculation We will come back to calculate the vector of the electric field from the scalar potential Phys272 - Spring 14 - von Doetinchem - 151

13 Electric force and electric potential Phys272 - Spring 14 - von Doetinchem - 154

14 Electric force and electric potential Phys272 - Spring 14 - von Doetinchem - 155

15 Calculating electric potential Make a drawing Charge distribution known: scalar sum or integral over distribution If we know the electric field as function of the position or can determine it by, e.g., Gauss's law define potential to be zero at a convenient place, Whenever possible try using an energy approach (scalar) rather than a dynamics approach (vector) Make a small graph of the result does it make sense? Phys272 - Spring 14 - von Doetinchem - 156

16 Charged conducting sphere Electric field outside a sphere is the same as for a point charge Electric field inside the conducting sphere is zero no work is done if a test charge moves inside the sphere potential inside the sphere is the same as on the surface Phys272 - Spring 14 - von Doetinchem - 158

17 Van de Graaf generator Phys272 - Spring 14 - von Doetinchem - 159

18 Ionization and corona discharge Source: In air: charge cannot build up indefinitely electric field can become so strong that neutral air transforms into ionized air where charges can move air becomes conducting charges from the sphere go into the air maximum limit for charge depends on radius small wires or sharp objects allow easier discharge Lightning bolt rod has a blunt end to allow substantial charge buildup sharp ends would allow a smaller charge buildup Phys272 - Spring 14 - von Doetinchem - 160

19 Potential of a line of charge Phys272 - Spring 14 - von Doetinchem - 162

20 Equipotential surfaces Equipotential lines are similar to field lines they help us to visualize a potential Similar to a topographic map: line corresponds to same potential Electric field lines Equipotential lines Charge can be moved around this potential line Source: without exerting electric force force must be perpendicular to equipotential line field lines are perpendicular to potential lines Lines are closer to each other for steeper gradients Equipotential lines cannot intersect Electric field is generally not constant over an equipotential line Phys272 - Spring 14 - von Doetinchem - 163

21 Equipotentials and conductors Electric force is conservative it is not possible to do work on a test charge like that: Electric field lines are perpendicular to surface of conductor. Every potential difference inside a conductor is 0 surface must be at a constant potential In the electrostatic case the surface of a conductor is always an equipotential surface. Phys272 - Spring 14 - von Doetinchem - 164

22 Charge on surface of cavity with no charge inside cavity? Phys272 - Spring 14 - von Doetinchem - 166

23 Potential gradient Vector electric field can be calculated from scalar electric potential Potential gradient points towards the most rapid change in position. The shortest way to the next equipotential line is perpendicular to the old line: electric field perpendicular to equipotential lines Absolute value of potential is not important for electric field, only the local change. Phys272 - Spring 14 - von Doetinchem - 168

24 Potential gradient Phys272 - Spring 14 - von Doetinchem - 169

25 Potential and field of a point charge unit vector Phys272 - Spring 14 - von Doetinchem - 171

26 Review Electric potential energy: Electric force is conservative Work done by an electric force is represented by the change in potential energy Electric potential: Potential energy per unit charge Potential difference between two points equals the amount of work to move a test charge between those points. Potential difference between two points is given by the line integral along the electric field Equipotential lines are lines of constant potential. Electric field lines and equipotential lines are perpendicular. The electric field can be calculated from the potential gradient of the electric potential. Phys272 - Spring 14 - von Doetinchem - 172

27 Discussion 1) It is easy to produce a potential difference of several thousand volts between your body and the floor by scuffing your shoes across a nylon carpet. When you touch a metal doorknob, you get a mild shock. Yet contact with a power line of comparable voltage would probably be fatal. Why is there a difference? Potential is high on your body, but the amount of net charge is low The power line delivers much more electrons and the electrical energy is much higher. 2) A high-voltage DC power line falls on a car, so the entire metal body of the car is at a potential of 10,000V with respect to the ground. What happens to the occupants when they are sitting in the car? What happens when they step out? Everything is on the same potential when the persons sit in the car no potential gradient Stepping out while being in contact with the car is dangerous: many electrons will move into the ground following a high potential gradient 3) When a thunderstorm is approaching, sailors at sea sometimes observe a phenomenon called St. Elmo's fire, a bluish flickering light at the tips of the masts. Why is the effect pronounced when the masts are wet? Static electricity can place a net charge on the ship (did you ever notice your hairs standing up during an oncoming thunderstorm?) Light can appear as a discharge from the sharpest points like the top of the masts Seawater conducts well due to the salt and guides the charges to the discharge point Phys272 - Spring 14 - von Doetinchem - 174

28 Capacitance and dielectrics Capactior stores electric potential and electric charge Capacitor: just insulate two conductors (with same amount of negative and positive charge) Work must be done to move charges through the resulting potential stored electric potential energy Applications: flashs, electronic devices Capacitor has a certain capacitance depending on its properties: size, shape, material Capacitance increases when using an insulating material between the negative and positive side (polarization) Electric field can be seen as a store-house of electric potential energy Phys272 - Spring 14 - von Doetinchem - 175

29 Capacitors and capacitance Charging capacitor: conductors initially uncharged Transfer electrons from one side to the other Net charge on capacitor is zero Common way of charging: connect sides to different terminals of a battery Electric field is proportional to the stored charge (the same is true for the potential difference) Capacitance stays constant: Capacitance is a measure of the ability of a capacitor to store energy. Phys272 - Spring 14 - von Doetinchem - 176

30 Calculating capactiance: capacitors in vacuum Nothing between oppositely charged conductors condenser microphone: capacitance changes due to flexible plate moved by sound waves current flow One farad is a very large amount: typical values: flash unit in a camera: microfarad (µf, 10-6) radio tuning unit: picofarad (pf, 10-12) Phys272 - Spring 14 - von Doetinchem - 177

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