Electric and Magnetic Fields

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
• Kc9x109 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
Calculating the force from an 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!!

10
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?

11
Sample Problem p. 647 3

• E 2.0 x 104 N/C , q 1.6 x 10-19 C
• FqE 3.2 x 10-15 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 theres a
  positive charge to the left

12
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 10-15 N along the positive x axis
  (to the right)

13
For the electron

• Since theres 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 10-15 N along the negative x axis
  (to the left)

14
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

15
Sample Problem p. 656 38

• For the 30 nC charge
• Direction of the E-field for both charges is
  away since theyre both positive

• For the 60 nC charge

16
Which one will win?

• At the midway point, the 30nC charges field
  strength is 12000 N/C toward the 60 nC charge and
  the 60 nC charges field strength is 24,000 N/C
  toward the 30 nC charge.
• The 60 nC charge will win. Since the fields
  point in opposite directions, you have to
  subtract
• Answer 12,000 N/C toward the 30 nC charge

17
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

18
Answer ?

• FqE(1.6x10-19 C)(2.0 x 103 N/C)
• 3.2 x 10-16 N
• Direction?
• Answer 3.2 x 10-16 N along the positive x-axis
  (to the right)

19
Answer ?

• B. What is the acceleration?
• Ask Newton!
• Fma
• a F/m 3.2 x 10-16 N/1.6x10-27 kg
• a 2 x 1011 m/s2 along the positive x axis

20
Magnetism!
21
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

22
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)

23
Magnetic Field of the Earth

• The Earths 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 Earths geographic pole is magnetic
  south

24
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

25
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

26
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)

27
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

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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, youll have to use the rule and
change the sign!
Direction of Field Symbol
Into the page X
Out of the page
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Examples
Direction of F Direction of v Direction of B Sign of Charge
Out of the page East North
Into the page East North -
Out of the page West South
Into the page West South -
South West Into the page
South West Out of the page -
East North Out of the page
South Out of the page East -
Out of the page South West -
Into the page west North
30
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 10-12 N, find the
  speed of the proton. What is the direction of the
  force exerted on the proton?

31
The speed of the proton

• Whats the direction of F? Use the RHR!!
• v is east, B is northF is.
• Out of the page!
• If it was an electron, the force would be into
  the page!

32
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.

33
Sample Problem (not in book)

• F 2.88 x 10-12 N
• Direction? Use the RHR
• V points west, B points out of the page
• F points SOUTH (remember its an electron!!)