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Physics 2102 Jonathan Dowling. Physics 2102 Lecture: 07 TUE 09 FEB. Electric Potential II. 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!. - PowerPoint PPT Presentation

Physics 2102 Lecture: 07 TUE 09 FEBElectric Potential II

PHYS2102 FIRST MIDTERM EXAM!67PM THU 11 FEB 2009Dowlings 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:http://www.phys.lsu.edu/classes/spring2010/phys2102/formulasheet.pdf KNOW SI PREFIXES n, cm, k, etc.

Conservative Forces, Work, and Potential Energy

Coulombs Law for Point ChargeP1P2q1q2P1P2q2

Continuous Charge DistributionsDivide the charge distribution into differential elementsWrite down an expression for potential from a typical element treat as point chargeIntegrate!Simple example: circular rod of radius r, total charge Q; find V at center.dqr

Potential of Continuous Charge Distribution: Line of Charge Uniformly charged rodTotal charge QLength LWhat is V at position P?PUnits: [Nm2/C2][C/m]=[Nm/C]=[J/C]=[V]

Electric Field & Potential: A Simple Relationship!Notice the following:Point charge:E = kQ/r2V = kQ/rDipole (far away):E = kp/r3V = kp/r2E 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)

E from V: Example Uniformly charged rodTotal charge QLength LWe Found V at P!Find E from V?P

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

+qOutside the sphere: Replace by point charge!Inside the sphere: E =0 (Gauss Law) E = dV/dr= 0 IFF V=constantElectric Field & Potential: Example

Equipotentials and ConductorsConducting surfaces are EQUIPOTENTIALs At surface of conductor, E is normal (perpendicular) to surfaceHence, 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.EV

Conductors Change the Field Around Them!

Sharp ConductorsCharge density is higher at conductor surfaces that have small radius of curvatureE = s/e0 for a conductor, hence STRONGER electric fields at sharply curved surfaces!Used for attracting or getting rid of charge: lightning rodsVan de Graaf -- metal brush transfers charge from rubber beltMars 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 CROUCHIf 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 = VoltElectric potential uniquely defined for every point in space -- independent of path!Electric potential is a scalar -- add contributions from individual point chargesWe calculated the electric potential produced by a single charge: V=kq/r, and by continuous charge distributions : V=kdq/rElectric field and electric potential: E= -dV/dxElectric 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.