Announcements – 272H EXAM 1 – Thursday, Feb. 13, 8-9:30 pm in room 203 –Chapters 14, 15, & 16 –Equation sheet will be provided –Pencil, calculator There will be no lecture on Monday Feb. 17

ABCDEABCDE is equal Clicker Question

General Procedure for Calculating Electric Field of Distributed Charges 1.Cut the charge distribution into pieces for which the field is known 2.Write an expression for the electric field due to one piece (i) Choose origin (ii) Write an expression for  E and its components 3.Add up the contributions of all the pieces (i) Try to integrate symbolically (ii) If impossible – integrate numerically 4.Check the results: (i) Direction (ii) Units (iii) Special cases

A total charge Q is uniformly distributed over a half ring with radius R. The total charge inside a small element dθ is given by: 1.Choice One 2.Choice Two 3.Choice Three 4.Choice Four 5.Choice Five 6.Choice Six θ dθdθ Q R A. B. C. D. E. Clicker Question

A total charge Q is uniformly distributed over a half ring with radius R. The Y component of electric field at the center created by a short element dθ is given by: 1.Choice One 2.Choice Two 3.Choice Three 4.Choice Four θ dθdθ Q R A. B. C. D. +y Clicker Question

Section 15.5 – home study! A Uniformly Charged Disk

Uniformly Charged Disk Edge On Can a conducting disk have uniform charge distribution? A single metal disk cannot be uniformly charged: charges repel and concentrate at the edges

A Uniformly Charged Disk Close to the disk (0 < z < R) Along z axis Approximations: If z/R is extremely small Very close to disk (0 < z << R)

Field Far From the Disk Exact For z>>R Point Charge

Two disks of opposite charges, s<<R: charges distribute uniformly: +Q+Q-Q-Q s We will calculate E both inside and outside of the disk close to the center Two uniformly charged metal disks of radius R placed very near each other Almost all the charge is nearly uniformly distributed on the inner surfaces of the disks; very little charge on the outer surfaces. Capacitor Why must there be charge on the outer surfaces?

+Q+Q-Q-Q s We know the field for a single diskThere are only 2 “pieces” E-E- E+E+ E net Step 1: Cut Charge Distribution into Pieces

Step 2: Contribution of one Piece Origin: left disk, center E-E- E+E+ E net s z 0 Location of disks: z=0, z=s Distance from disk to  2 z, (s-z) Left: Right:

Step 3: Add up Contributions E-E- E+E+ E net s z 0 Location:  2 (inside a capacitor)  Does not depend on z

Step 3: Add up Contributions E-E- E+E+ E net s z 0 Location:  3 (fringe field) For s<<R: E 1 =E 3  0 Far from the capacitor (z>>R>>s): E 1 =E 3 ~1/z 3 (like dipole) Fringe field is very small compared to the field inside the capacitor.

E-E- E+E+ E net s z 0 Units:  Inside: Fringe: Step 4: check the results: Electric Field of a Capacitor

Given: capacitor, radius R=50 cm, gap s=1 mm (air). Find: maximum charge before sparks are formed (E crit =3  10 6 N/C) Solution: What Q would cause sparking if spacing s  2s? What is the attractive force between the plates? F=QE= (2.1  C)(3  10 6 N/C)=63 N F=Q(E crit /2)= (2.1  C)(3  10 6 /2 N/C)=31.5 N Exercise

Field inside: Field outside:(like point charge)  Qualitative approach  Integration Electric Field of a Spherical Shell of Charge

E 1 +E 4 E2E2 E3E3 E6E6 E5E5 Divide into 6 areas: Direction: radial- due to the symmetry  E of a Sphere Outside

Magnitude:  How would a charged sphere interact with other charges? - as a point charge (same force) E of a Sphere Outside As long as we are far from a region of distributed charges we can approximate the electric field of that region as being due to a point charge.

Magnitude: E=0  Note: E is not always 0 inside – other charges in the Universe may make a nonzero electric field inside. E of a Sphere Inside

E=0: Implications Fill charged sphere with plastic. Will plastic be polarized? No! Solid metal sphere: since it is a conductor, any excess charges on the sphere arranges itself uniformly on the outer surface. There will be no field nor excess charges inside! In general: In static equilibrium, there is no electric field inside metals E of a Sphere Inside

What is electric field right at the surface? Need to be >1000 atomic diameters away from surface for equations to work! E of a Sphere Inside Electric field at the surface is highly variable in magnitude and direction