What is the electric potential difference (V, volt) between the cloud and the earth? Ecritical = 3*106 N/C A) 3*109 B) 3*106 C) 1010 - - 1 km + +

Potential in Metal In static equilibrium A Capacitor with large plates and a small gap of 3 mm has a potential difference of 6 Volts from one plate to the other. E d =3 mm +Q -Q -3 V +3 V Charges are on surface V = 6 Volt

Question 300 V/m 0 V/m 300 V/m A B 0.02m 0.03m 0.04m What is VB-VA? D What is VB-VA? 270 V -270 V -18 V 6 V -6 V

Question 0 V/m A B 0.02m 0.03m 0.04m x D VB-VA = -300*(0.02-0) - (-300)*(0.09-0.05)=-6+12 V = +6 V

Potential in Metal In static equilibrium Insert a 1 mm thick metal slab into the center of the capacitor. d =3 mm +Q1 -Q1 1 mm Metal slab polarizes and has charges +Q2 and -Q2 on its surfaces. What are the charges Q1 and Q2? Q2=Q1 E inside metal is zero  Now we have 2 capacitors instead of one E inside metal slab is zero! V = 4 V V inside metal slab is zero! Charges +Q2 and –Q2 There is no “conservation of potential”!

Potential in Metal Not in static equilibrium Metal is not in static equilibrium: When it is in the process of being polarized When there is an external source of mobile charges (battery) Nonzero electric field of uniform magnitude E throughout the interior of a wire of length L. Direction of the field follows the direction of the wire. For each step, the potential difference is: V = -EL But in a circuit a thick copper wire may have a very small electric field. B is at lower potential than A.

Electric Field and Potential If we know electric field ( ) everywhere we can compute potential (V) in every point in space. Can we compute ( ) if we know V?

Exercise Suppose in some area of space V(x,y,z)=x2+yz. What is E(x,y,z)?

Round Trip Potential Difference + Potential difference due to a stationary point charge is independent of the path A vector field is a conservative field if we can find a potential (scalar function) so that the vector field is the gradient of the potential. Potential difference along a closed loop is zero A vector field is a conservative field if we can find a potential (scalar function) so that the vector field is the gradient of the potential.

Predicting Possible Field Configuration Is the following “curly” pattern of electric field possible? dl dl is always parallel to Cannot produce with any stationary arrangement of charges – but could be in principle, will talk in later chapters. Move from A to A dl This “curly” pattern of electric field is impossible to produce by arranging any number of stationary point charges!

Wire in a Circuit and Electric Field In a current-carrying wire in a circuit, there can be a nonzero electric field, so there is a difference in potential between two locations in the wire. Electric field is not confined to wire in a circuit – there is E around! Electric field is not confined to the wire in a circuit – there must be an electric field E around the wire in the air!

Potential of a Uniformly Charged Ring Q Method 1: Divide into point charges and add up contributions due to each charge

Potential of a Uniformly Charged Ring Q Method 2: Integrate electric field along a path Note that we integrate from an initial z=infinity to a final z so that V represents the energy per unit charge required to move a point charge in from infinity to z.

Potential of a Uniformly Charged Ring Q What is V for z>>R ? Is it unexpected? The same as for a point charge!

Exercise How much work one needs to do to bring a point charge q from infinity into the center of the uniformly charged (Q) hollow sphere of radius R? k*Q*q/R2 k*Q*q/R k*Q*q/(4pR2) Not enough information Q R

Exercise What is the potential in the center of uniformly charged hollow sphere? R Add contribution from each point charge on the surface.

Potential Inside a Uniformly Charged Hollow Sphere =0

The difference between metals and insulators +Q -Q insulator metal -Q +Q E inside insulator is non zero E inside metal =

Dielectric Constant Electric field in capacitor filled with insulator: Enet=Eplates-Edipoles -Q +Q -q +q - + qdipoles = b*Q Alpha is small. K – dielectric constant

Dielectric Constant Inside an insulator: Dielectric constant for various insulators: vacuum 1 (by definition) air 1.0006 typical plastic 5 NaCl 6.1 water 80 strontium titanate 310

Potential Difference in a Capacitor with Insulator demonstration s

Potential Difference in Partially Filled Capacitor K -Q +Q Talk if time permits – skip with no consequences. Note that we ignore the electric field due to the dielectric in the vacuum region. s A B x