1. Which graphical representation of electric field of a point charge
is correct?
E) I do not know A B _ + C D + _

2. Point charge does not exert field on itself!_
What if the magnitude of electric field exactly at the position of a point charge?
Point charge does not exert field on itself!

3. The Superposition Principle
The net electric field at a location in space is a vector sum of the individual electric fields contributed by all charged particles located elsewhere.
The electric field contributed by a charged particle is unaffected by the presence of other charged particles.

4. The Superposition Principle
If many more point charges are present (qi) we go for i i
and eventually for integral  !

5. System consists of two point charges (+4) and (+1)
How many points exist in space where E-field is equal zero?
None
One
Two
Infinite number
I don’t know +4 +1

6. E-field in the middle of uniformly positively charge ring is represented by
Red arrow
Blue arrow
Zero
I do not know x y
What is about any other point
inside the ring?

7. The E of a Uniformly Charged Sphere
Can calculate using principle of superposition:
for r>R (outside)
Uniformly charged sphere acts like a point charge! Not only its field is the same (outside), but it also interacts with other charge particles as a point charge.
for r<R (inside)

8. The Superposition Principle
The electric field of a dipole:
Electric dipole:
Two equally but oppositely charged point-like objects +q -q s
Example of electric dipole: HCl molecule
What is the E field far from the dipole (r>s)?

9. Dipoles are ubiquitous
Atom will become dipole when it experiences electric field:
Some molecules exist in the form of permanent dipoles:
HCl molecule

10. In Protein the carbonyl groups of polypeptides have substantial dipole moments and their electrostatic interactions make an important energetic contribution to the stability of an a-helix O C
D=3.7 Debye - +

11. Calculating Electric Field
Choice of the origin x y z +q -q s
Choice of origin: use symmetry

12. 1. E along the x-axis

13. Approximation: Far from the Dipole
if r>>s, then
While the electric field of a point charge is proportional to 1/r2, the electric field created by several charges may have a different distance dependence.

14. 2. E along the y-axis

15. 2. E along the y-axis if r>>s, then at <0,r,0>
Ask now about coordinate <0,0,r> - make them think about symmetry.
if r>>s, then
at <0,r,0>

16. 3. E along the z-axis at <r,0,0> at <0,r,0>
or <0,0,r>
Point out difference – direction and magnitude
Due to the symmetry E along the z-axis must be the same as E along the y-axis!

17. Other Locations
Ask students where is + and where is -.

18. The Electric Field y x z Point Charge: Dipole: s -q +q + -
for r>>s :
at <r,0,0>
at <0,r,0> +q -q s x y z
at <0,0,r>
Note that the magnitude of the electric field at a location along the y axis is HALF of the magnitude of the electric field at a location the same distance away on the x axis!

19. System consists of two point charges (+1) and (-1)
How many points exist in space where E-field is equal zero?
None
One
Two
Infinite number
I don’t know +1 -1

20. Dipole in a Uniform Field
Forces on +q and –q have the same magnitude but opposite direction
It would experience a torque about its center of mass.
What would be equi
What is the equilibrium position?
Electric dipole can be used to measure the direction of electric field.

21. Dipole Moment x: r>>s y, z:
The electric field of a dipole is proportional to the
Dipole moment: p = qs
Note – aproximate
, direction from –q to +q
Dipole moment is a vector pointing from negative to positive charge

22. Electric Field
[N/C]
Electric field has units of Newton per Coulomb:

23. A Fundamental Rationale
Convenience: know E at some location – know the electric force on any charge:
Can describe the electric properties of matter in terms of electric field – independent of how this field was produced.
Example: if E>3106 N/C air becomes conductor
Retardation
Nothing can move faster than light c
c = 300,000 km/s = 30 cm/ns
Coulomb’s law is not completely correct – it does not contain time t nor speed of light c.
Example: Suppose I am negatively charged sphere, move to one side ask student in back row to show the direction of E due to this charge.
Then move to the other side at ~speed of light and ask student what will happen to E. It is ~5 meters, so it takes 15 ns for E to change direction after I moved!
More drastic example – pretend that I hold electron and positron (dipole), ask student to show E. Collapse (annihilate) charges and count time.
Conclusion: E can exist independently of charges!!!
Does not contain v – works only when speed is << c
v<<c !!!

24. Example Problem y E=? Since r>>s: 200Å x
A dipole is located at the origin, and is composed of particles with charges e and –e, separated by a distance 210-10 m along the x-axis. Calculate the magnitude of the E field at <0,210-8,0> m.
E=?
Since r>>s:
200Å x
A dipole is located at the origin, and is composed of particles with charge e and –e, separated by a distance 210-10 m along the x-axis. Calculate the magnitude of the E field at <0,210-8,0> m. 2Å
Using exact solution:

25. Interaction of a Point Charge and a Dipole
Direction makes sense?
- negative end of dipole is closer, so its net contribution is larger
What is the force exerted on the dipole by the point charge?
- Newton’s third law: equal but opposite sign
Why is it possible? Total charge of dipole is zero! – the key lays in distance dependence