1. Electric and Magnetic Fields
Chapters 17 & 21

2. Electric Field
Electric force, like gravitational force, is a field force
Remember: Field forces can act through space even when there is no physical contact between the objects involved
A charged object has an electric field in the space around it

3. Electric Field Lines
Electric Field Lines point in the direction of the electric field
The number and spacing of field lines is proportional to the electric field strength
The electric field is strong where the field lines are close together and weaker when they are far apart

4. Electric Field Lines
The lines for a positive charge point away from the charge
The lines for a negative charge point towards the charge

5. Electric Field Lines
This diagram shows the electric field lines for two equal and opposite point charges
Notice that the lines begin on the positive charge and end on the negative charge

6. Electric Field Lines
This diagram shows the electric field lines for two positive point charges
Notice that the same number of lines emerges from each charge because they are equal in magnitude

7. Electric Field Lines
If the charges are unequal, then the number of lines emerging from them will be different
Notice that the positive charge has twice as many lines

8. Calculating Electric Field Strength
The equation for the electric field produced by a point charge is:
Kc=9x109 Nm2/C2 ,r is the distance from the charge and q is the charge producing the field
The unit for E is N/C
Electric field strength is a vector!!
If q is positive, then E is directed away from q
If q is negative, then E is directed toward q

9. Sample Problem p. 647 #3
An electric field of 2.0 x 104 N/C is directed along the positive x-axis
a. What is the electric force on an electron in this field?
b. What is the electric force on a proton in this field?

10. Sample Problem p. 647 #3 E= 2.0 x 104 N/C , q= 1.6 x 10-19 C
F=qE= 3.2 x N for both the electron and the proton
What about the direction?
The electric field is pointing along the positive x axis (to the right) which means there’s a positive charge to the left
E field +

11. For the proton
Since the electric field is pointing to the right, if you put a proton in it, the proton will want to move away towards the right and the direction of the force on it will be to the right
Answer: 3.2 x N along the positive x axis (to the right) + F +

12. For the electron
Since there’s a positive charge causing the electric field to point towards the right, an electron would feel attracted to the positive charge. Therefore, the force acting on it is toward the left
Answer: 3.2 x N along the negative x axis (to the left) - F +

13. Sample Problem p. 656 #38
Find the electric field at a point midway between two charges of +30 nC and 60 nC separated by a distance of 30.0 cm
+30 nC
+60 nC

14. Sample Problem p. 656 #38 For the 30 nC charge:
Direction of the E-field for both charges is “away” since they’re both positive
For the 60 nC charge:
+30 nC
+60 nC

15. Which one will win?
At the midway point, the 30nC charge’s field strength is N/C toward the 60 nC charge and the 60 nC charge’s field strength is 24,000 N/C toward the 30 nC charge.
The 60 nC charge will win. Since the field’s point in opposite directions, you have to subtract
Answer: 12,000 N/C toward the 30 nC charge

16. Sample Problem (p.659 #66)
A constant electric field directed along the positive x-axis has a strength of 2.0 x 103 N/C.
Find the electric force exerted on a proton by the field
Find the acceleration of the proton

17. Answer  F=qE=(1.6x10-19 C)(2.0 x 103 N/C)= Direction? 3.2 x 10-16 N
Answer: 3.2 x N along the positive x-axis (to the right)
E field + + F

18. Answer  B. What is the acceleration? Ask Newton! F=ma
a = F/m= 3.2 x N/1.6x10-27 kg
a= 2 x 1011 m/s2 along the positive x axis

19. Field strength of the uniform field between charged parallel plates

20. Formula

21. Calculating the force from a uniform electric field
If a charged object is placed in an electric field, we can calculate the force acting on it from the electric field
Remember that F is a vector!!

22. Motion of Charged Particles in a Uniform Electric Field
When a particle of charge ‘q’ and mass ‘m’ is placed in an electric field ‘E’, the electric force exerted on the charge is qE.
If this is the only force exerted on the particle, it must be the net force and so must cause the particle to accelerate.
In this case, Newton’s second law applied to the particle gives

23. The acceleration of the particle is therefore electric force on the charge particles
E is uniform (that is, constant in magnitude and direction), then the acceleration is constant. If the particle has a positive charge, then its acceleration is in the direction of the electric field. If the particle has a negative charge, then its acceleration is in the direction opposite the electric field.

30. Magnetism!

31. Magnets The ends of a bar magnet are called poles
Like poles repel and unlike poles attract
Regardless of their shape, all magnets have a north and south pole

32. Magnetic Fields
Magnetic Field lines point from the north pole to the south pole of the magnet
The north pole of a compass needle always points in the direction of the field (from North to South)

33. Magnetic Field of the Earth
The Earth’s geographic North pole is actually the magnetic south pole
The north pole of a compass points towards geographic north and since opposites attract, we know that the Earth’s geographic pole is magnetic south

34. Magnetic Field of a wire
Moving charges produce magnetic fields
If there is a current moving through a wire, a magnetic field is produced around the wire

35. Magnetic Field of a wire
The “Right Hand Rule” for the magnetic field
Point your thumb in the direction of the current and curl your fingers in the direction of the field

36. Magnetic Force
A charge moving through a magnetic field experiences a force
q= magnitude of charge
v= speed of charge
B= Strength of the magnetic field (measured in Tesla, T)

37. A second Right-Hand Rule
Of course, force is a vector!
To find the direction of the magnetic force use another right hand rule
Fingers point in direction of the field
Thumb points in direction of v
Palm points in direction of magnetic force

38. Conventions for direction of field
WARNING: The right hand rule is for the
direction of the force acting on a POSITIVE
CHARGE.
To find the direction of the force acting on a negative charge, you’ll have to use the rule and change the sign!
Direction of Field
Symbol
Into the page X
Out of the page

39. Examples Direction of F Direction of v Direction of B Sign of Charge
Out of the page
East
North +
Into the page -
West
South
west

40. Sample Problem p. 775 #2 (edited)
A proton traveling to the right along the x-axis enters a region where there is a magnetic field of 2.5 T directed north. If the proton experiences a force of 3.2 x N, find the speed of the proton. What is the direction of the force exerted on the proton?

41. The speed of the proton What’s the direction of F? Use the RHR!!
v is east, B is north…F is….
Out of the page!
If it was an electron, the force would be into the page!

42. Sample Problem (not in book)
An electron is moving with a velocity of 6 x 106 m/s westward in a 3.0 T magnetic field that is pointed out of the page.
Find the magnitude and direction of the force acting on the electron.

43. Sample Problem (not in book)
F= 2.88 x N
Direction? Use the RHR
V points west, B points out of the page…
F points SOUTH (remember it’s an electron!!)