Electric potential, Systems of charges

1. Electric potential,Systems of charges Physics 114 Lecture IV

2. Concepts • Primary concepts: • Electric potential • Electric energy • capacitance • Secondary concepts: • Equipotentials • Electonvolt Lecture IV

3. Potential electric energy High PE High PE Low PE Just like gravity electric force can do work work does not depend on the path it depends only on the initial and final position  there is a potential energy associated with electric field. Low PE Lecture IV

4. Electric potential • PE/q is a property of the field itself – called electric potentialV Lecture IV

5. Electric potential • V – electric potential is the potential energy of a positive test charge in electric field, divided by the magnitude of this charge q. • Electric potential is a scalar (so much nicer!). • Electric potential is measured in Volts (V=J/C). • Potential difference between two points DV=Vb-Va is often called voltage. Lecture IV

6. Charges in electric fields b E=const Force on charge q: F=qE Work done by the field to move this charge W=Fd=dqE W=PEa-PEb=qVa-qVb=-qDV • d E=DV • E= DV/d, points from high potential to low • Sometimes electric field is measured in V/m =N/C + a Lecture IV

7. Non-uniform electric field + Lecture IV

8. Determine E from V • Think ski slopes • If V depends on one coordinate x • E is directed along x from high V to low • If V depends on x,y,z Lecture IV

9. Electric field and potential in conductors E=0 in good conductors in the static situation. E is perpendicular to the surface of conductor. Metal hollow boxes are used to shield electric fields. When charges are not moving (!!) conductor is entirely at the same potential. + + + + + - - - - - Lecture IV

10. Electronvolt • Energy that one electron gains when being accelerated over 1V potential difference is called electronvolt eV: • 1eV=1.6x10-19C 1V= 1.6x10-19J • Yet another unit to measure energy, • Commonly used in atomic and particle physics. Lecture IV

11. Equipontentials Equipotentials • are surfaces at the same potential; • are always perpendicular to field lines; • Never cross; • Their density represents the strength of the electric field • Potential is higher at points closer to positive charge Lecture IV

12. Potential of a point charge Potential V of electric field created by a point charge Q at a radius r is Q>0  V>0 Q<0  V<0 Do not forget the signs! Potential goes to 0 at infinity. Equipotentials of a point charge are concentric spheres. + Lecture IV

13. Superposition of fields Principle of superposition: Net potential created by a system of charges is a scalar (!) sum of potentials created by individual charges: + + - 1 2 Potential is a scalar  no direction to worry about, But signs are important. Lecture IV

14. Work to move a charge How much work has to be done by an external force to move a charge q=+1.5 mC from point a to point b? Work-energy principle + 30cm + 20cm 15cm 25cm + - Q1=10mC Q2=-20mC Lecture IV

15. Capacitance • Two parallel plates are called a capacitor. When capacitor is connected to a battery plates will charge up. Note: net charge =0 • C – coefficient, called capacitance, property of the capacitor. • Capacitance is measured in Farad (F=C/V) Lecture IV

16. Electric field in a capacitor E=const • E= V/d • points from high potential to low • When V is fixed (same battery), E depends only on the d. • Potential • High next to + plate • Low – next to - plate Lecture IV

17. Capacitance • Capacitance depends on the geometry of a capacitor • e0 = 8.85. 10-12 C2/N m2- • permittivity of free space • A – area of plates (m2) • Same sign charges want to “spread out” – to hold more charge need large area • d – distance between plates (m) • Opposite sign charges “hold” each other, attraction is stronger for shorter d A d Lecture IV

18. Dielectrics • Put non-conductive material (dielectric) between plates • Can hold more charge  capacitance increases • K(>1) – dielectric constant Lecture IV

19. Charging up a capacitor • Find the work needed to charge a capacitor C to voltage V • Take small charge dq and move it across the capacitor, which is at voltage V at this moment • dW=Vdq Lecture IV

20. Energy storage • Work to charge a capacitor= potential energy stored in the capacitor • To use the right formula, watch what is kept constant • V=const – if C connected to a battery • Q=const - if C disconnected Lecture IV

21. Inserting dielectric • Capacitor is connected to a battery, supplying voltage V. How will the energy stored in the capacitor change if we insert a dielectric (K=2)? • CKC=2C – capacitance increases V stays const – same battery Q changes Lecture IV

22. Inserting dielectric • Capacitor is charged to charge Q and disconnected from a battery. How will the energy stored in the capacitor change if we insert a dielectric (K=2)? • CKC=2C – capacitance increases V can change Q stays const – charge conservation Lecture IV

23. Inserting dielectric Disconnected battery – energy decreases Dielectric will be “sucked in” Connected battery – energy increases Dielectric will be “pushed out” Lecture IV

24. Test problem • Between two very large oppositely charged parallel plates at which of the three locations A, B and C electric potential is the greatest? • A A • B B • C C • D Equal at all three locations. Lecture IV

25. E near metal sphere • Find the largest charge Q that a conductive sphere radius r=1cm can hold. • Air breakdown E=3x106V/m Larger spheres can hold more charge Lecture IV

26. Test problem • What is wrong with this picture? • A Equipotentials must be parallel to field lines • B Field lines cannot go to infinity • C Some field lines point away from the negative charge • D Equipotentials cannot be closed Lecture IV