Physics 212 Lecture 6 Electric Potential

V in Volts = Joules/Coulomb BIG IDEA Last time we defined the electric potential energy of charge q in an electric field: The only mention of the particle was through its charge q. We can obtain a new quantity, the electric potential, which is a PROPERTY OF THE SPACE, as the potential energy per unit charge. V in Volts = Joules/Coulomb The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class. Note the similarity to the definition of another quantity which is also a PROPERTY OF THE SPACE, the electric field. 40

Electric Potential from E field Consider the three points A, B, and C located in a region of constant electric field as shown. D Dx What is the sign of DVAC = VC - VA ? (A) DVAC < 0 (B) DVAC = 0 (C) DVAC > 0 Remember the definition: The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class. Choose a path (any will do!) 40

Checkpoint 2 A B C D Remember the definition V is constant !! 08

E from V We obtain the potential by integrating the electric field: So, we can obtain the electric field by differentiating the potential. In Cartesian coordinates: The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class. 40

Checkpoint 1a How do we get E from V?? Look at slopes !!! 08

Checkpoint 1b A B C D How do we get E from V?? Look at slopes !!! 08

Equipotentials Equipotentials are the locus of points having the same potential. Equipotentials produced by a point charge The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class. Equipotentials are ALWAYS perpendicular to the electric field lines The SPACING of the equipotentials indicates The STRENGTH of the electric field 40

Checkpoint 3a A B C D 08

Checkpoint 3b A B C D 08

HINT E - FIELD LINES A B C D EQUIPOTENTIALS What is work done by E field to move negative charge from A to C ? (A) WAC < 0 (B) WAC = 0 (C) WAC > 0 A B C D A and C are on the same equipotential WAC = 0 Equipotentials are perpendicular to the E field: No work is done along an equipotential. 08

Checkpoint 3b Again? A and C are on the same equipotential B and D are on the same equipotential Therefore the potential difference between A and B is the SAME as the potential between C and D 08

Checkpoint 3c A B C D A B C D 08

What is V(r) as a function of r? cross-section a4 a3 +Q Point charge q at center of concentric conducting spherical shells of radii a1, a2, a3, and a4. The inner shell is uncharged, but the outer shell carries charge Q. What is V(r) as a function of r? a2 a1 +q metal metal - Charges q and Q will create an E field throughout space The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class. Spherical symmetry: Use Gauss’ Law to calculate E everywhere Integrate E to get V 40

r > a4 : What is E(r)? (A) 0 (B) (C) (D) (E) +Q +q r Why? Gauss’ law: r a4 a3 +Q r > a4 : What is E(r)? (A) 0 (B) (C) a2 a1 +q (D) (E) metal metal The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.

a3 < r < a4 : What is E(r)? +Q a3 < r < a4 : What is E(r)? (A) 0 (B) (C) r Applying Gauss’ law, what is Qenclosed for red sphere shown? (A) q (B) –q (C) 0 a2 a1 +q (D) (E) metal metal The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class. How is this possible??? -q must be induced at r=a3 surface charge at r=a4 surface = Q+q

+q metal +Q a1 a2 a3 a4 The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.

Just like a point charge ! +q metal +Q a1 a2 a3 a4 First find V(r) for r  a4 For r  a4 Just like a point charge ! So…

V( r ) constant inside a conductor ! +q metal +Q a1 a2 a3 a4 How about V(r) for ? V( r ) constant inside a conductor !

+q metal +Q a1 a2 a3 a4 V(r) for ?

+q metal +Q a1 a2 a3 a4 V(r) for ?

+q metal +Q a1 a2 a3 a4 V(r) for ?

Summary V a1 a2 a3 a4 r The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.