Electric Potential II Physics 2102 Jonathan Dowling Physics 2102 Lecture: 07 TUE 09 FEB

PHYS2102 FIRST MIDTERM EXAM! 6–7PM THU 11 FEB 2009 Dowling’s Sec. 4 in ??? YOU MUST BRING YOUR STUDENT ID! YOU MUST WRITE UNITS TO GET FULL CREDIT! The exam will cover chapters 21 through 24, as covered in homework sets 1, 2, and 3. The formula sheet for the exam can be found here: KNOW SI PREFIXES n, cm, k, etc.

Conservative Forces, Work, and Potential Energy Work Done (W) is Integral of Force (F) Potential Energy (U) is Negative of Work Done Hence Force is Negative Derivative of Potential Energy

Coulomb’s Law for Point Charge P1P1 P2P2 q1q1 q2q2 P1P1 P2P2 q2q2 Force [N] = Newton Potential Energy [J]=Joule Electric Potential [J/C]=[V] =Volt Electric Field [N/C]=[V/m]

Continuous Charge Distributions Divide the charge distribution into differential elements Write down an expression for potential from a typical element — treat as point charge Integrate! Simple example: circular rod of radius r, total charge Q; find V at center. dq r

Potential of Continuous Charge Distribution: Line of Charge Uniformly charged rod Total charge Q Length L What is V at position P? P x L a dx Units: [Nm 2 /C 2 ][C/m]=[Nm/C]=[J/C]=[V]

Electric Field & Potential: A Simple Relationship! Notice the following: Point charge: E = kQ/r 2 V = kQ/r Dipole (far away): E = kp/r 3 V = kp/r 2 E is given by a DERIVATIVE of V! Of course! Focus only on a simple case: electric field that points along +x axis but whose magnitude varies with x. Note: MINUS sign! Units for E: VOLTS/METER (V/m) Note: MINUS sign! Units for E: VOLTS/METER (V/m)

E from V: Example Uniformly charged rod Total charge Q Length L We Found V at P! Find E from V? P x L a dx Units: √ Electric Field!

Electric Field & Potential: Question Hollow metal sphere of radius R has a charge +q Which of the following is the electric potential V as a function of distance r from center of sphere? +q V r r=R (a) V r r=R (c) V r r=R (b)

+q Outside the sphere: Replace by point charge! Inside the sphere: E = 0 (Gauss’ Law) E = –dV/dr = 0 IFF V=constant V Electric Field & Potential: Example E

Equipotentials and Conductors Conducting surfaces are EQUIPOTENTIALs At surface of conductor, E is normal (perpendicular) to surface Hence, no work needed to move a charge from one point on a conductor surface to another Equipotentials are normal to E, so they follow the shape of the conductor near the surface. E V

Conductors Change the Field Around Them! An Uncharged Conductor: A Uniform Electric Field: An Uncharged Conductor in the Initially Uniform Electric Field:

Sharp Conductors Charge density is higher at conductor surfaces that have small radius of curvature E =   for a conductor, hence STRONGER electric fields at sharply curved surfaces! Used for attracting or getting rid of charge: –lightning rods –Van de Graaf -- metal brush transfers charge from rubber belt –Mars pathfinder mission -- tungsten points used to get rid of accumulated charge on rover (electric breakdown on Mars occurs at ~100 V/m) (NASA)

Ben Franklin Invents the Lightning Rod!

LIGHTNING SAFE CROUCH If caught out of doors during an approaching storm and your skin tingles or hair tries to stand on end, immediately do the "LIGHTNING SAFE CROUCH ”. Squat low to the ground on the balls of your feet, with your feet close together. Place your hands on your knees, with your head between them. Be the smallest target possible, and minimize your contact with the ground.

Summary: Electric potential: work needed to bring +1C from infinity; units = V = Volt Electric potential uniquely defined for every point in space -- independent of path! Electric potential is a scalar -- add contributions from individual point charges We calculated the electric potential produced by a single charge: V = kq/r, and by continuous charge distributions : V =  kdq/r Electric field and electric potential: E= -dV/dx Electric potential energy: work used to build the system, charge by charge. Use W = U = qV for each charge. Conductors: the charges move to make their surface equipotentials. Charge density and electric field are higher on sharp points of conductors.