1. 22-4 Coulomb’s Law q1 Unit q2 Only apply to point charges r
Force is a vector
Direction is along the line joining two particles
Attractive/repulsive for unlike/like charges

2. Coulomb’s Law: Example
Consider the forces between the proton and the electron in hydrogen atom in the ground state (lowest energy) where the distance between is 0.53x10-10 m.
Gravitational force
Observations:
At atomic level, one may ignore gravitational force
Atoms are stable because of strong electrical interaction
we typically experience gravitational force or electrical force
Back to the soda can experiment
Can you make soda can positively charged

3. Superposition Principle
In a system with multiple charge particles, the net force on one particle due to other charges (two or more) is the vector sum of each force due to each individual charge, and each individual contribution is unaffected by the presence of the other charge

4. Superposition Principle: an example
Assume q2 and q3 carry same type of charges but opposite to q1, calculate the total force on q1 q1 q3 q2
Step 1: calculate F12
Step 2: calculate F13
Step 3: calculate F q1 q2 q1 q3

5. 23-2 Electric Field Unit for E: N/C
Again, only applies to point charges
What is field?
A “field” is any physical quantity that has a value at every location in space. Its value can scalar (scalar field) or a vector (vector field).
Scalar Field: Temperature T(x,y,z)
Vector Field: Air flow in a room V(x,y,z)

6. 23-2 Electric Field: cont. E field is a vector
Measure an E field. Using a test charge q2 and measure the force acting on q2。
Superposition principle is valid.

7. Concept Check The E field at point P 1. along +x+q -q P x y
The E field at point P
1. along +x
2. along –x
3. along +y
4. along –y
5. another direction
Field line: always goes from positive to negative charges
direction of field: tangent to field line
strength of field: density of field line per unit area

8. Field of Continuous Charge Distribution
Evaluate the contribution from a small charge element: dq, dE
Don’t choose a special point
Don’t perform detailed calculation
Do decompose the dE into components: || and  to the symmetric axis. (coordinate)
2. Exploit symmetry: if one component is zero, do not calculate it.

9. Concept Check: Symmetry
What is the direction of E at point P?
1. Up
2. Down
3. Left
4, Right
5. None of above + P P + -
3. Set up integral: need to evaluate dq and express it in terms of a position parameter.

10. Quiz 2 (2/26/01, Friday)
Two charges are fixed on the perimeter of a circular clock face. +Q is placed at 2 o'clock; +2Q is at 12 o'clock.
Where should a third charge be placed on the perimeter so that the electric field is zero at the center (point P)?
What relative charge strength is required at that point for the electric field to be zero?

11. Gauss’ Law
Quantitative relationship between electric field (direction and magnitude) on a CLOSED SURFACE (Gaussian surface) and total charges inside the Gaussian surface.

12. Flux of Electric Field Measures how much field through a surface
Direction of surface (dA): normal to the surface
Flux is a function of E, A, and .
Therefore, =0 does not necessarily mean E=0.

13. Apply Gauss’s law r L
Two types of Gaussian Surfaces: r

14. Apply Gauss’s law 1. Point of interest has to be on Gaussian surface
2. Choose Gaussian surface so that E can be taken out of integration: explore the symmetry of E
E are the same everywhere on surface (sphere), often =0 or 180 so that cos0=1 or cos180=-1
E  surface (align on the surface): cos90=0
Combination (cylinder)
Symmetry of E
Gaussian Surface
Spherical (point & spherical charges)
Sphere
Cylindrical (line charge)
Cylinder
Planar (sheet of charge)
Box or cylinder

15. Apply Gauss’s law
3. Add all charges inside Gaussian Surface: algebraic sum
1<0
2 >0
+qoutside
4. Calculate E.

16. Concept Check: Gauss’ lawB -q +q p +q p +q p
Which situation has more electric flux through the closed surface?
Which situation has the largest E at the point P?

17. Gauss’ Law: Important Properties of Metals
In a static (no charge motion) condition, there cannot be excess charges in the interior of a metal, all excess charges must be on the surface
An equivalent statement: Ein=0

18. Quiz 3 (2/23/01)
In the figure, a small ball of mass m=1.0 mg and charge q = 2.0 10-8 C stays still 1 cm above a uniformly charged sheet (ignore the thickness). Assuming the sheet extends far horizontally and into and out of page, calculate the surface charge density s of the sheet.
m, q
1 cm