Electric and Magnetic
Fields
Chapters 17 & 21
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
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
Electric Field Lines

The lines for a positive charge point away from
the charge

The lines for a negative charge point towards
the charge
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
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
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
Calculating Electric Field
Strength

The equation for the electric field produced by a
point charge is:
kq
E



c
2
r
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
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
F  qE

Remember that F is a vector!!
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?
Sample Problem p. 647 #3

E= 2.0 x 104 N/C , q= 1.6 x 10-19 C
F=qE= 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 there’s a positive
E field
charge to the left
+
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
+

+
F
Answer: 3.2 x 10-15 N along the positive x axis
(to the right)
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
+

F
-
Answer: 3.2 x 10-15 N along the negative x axis
(to the left)
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
Sample Problem p. 656 #38

For the 30 nC charge:


kc q
9 x109 (30 x10 9 )
N
E 2 

12
,
000
r
C
0.15m 2


For the 60 nC charge:


kc q
9 x109 (60 x10 9 )
N
E 2 

24
,
000
r
C
0.15m 2
Direction of the E-field for both charges is “away”
since they’re both positive
+30 nC
+60 nC
Which one will win?

At the midway point, the 30nC charge’s field
strength is 12000 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
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

Answer 

F=qE=(1.6x10-19 C)(2.0 x 103 N/C)=


3.2 x 10-16 N
Direction?
E field
+
+
F
Answer: 3.2 x 10-16 N along the positive x-axis (to the
right)
Answer 

B. What is the acceleration?

Ask Newton!
F=ma
 a = F/m= 3.2 x 10-16 N/1.6x10-27 kg
 a= 2 x 1011 m/s2 along the positive x axis

Magnetism!
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

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)
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
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
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
Magnetic Force

A charge moving through a magnetic field
experiences a force
Fmagnetic  qvB
q= magnitude of charge
v= speed of charge
B= Strength of the magnetic field (measured in Tesla, T)
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

Conventions for direction of field
Direction
of Field
Symbol
Into the
page
X
Out of the
page
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!
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
+
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?
The speed of the proton
v

Fmagnetic
qB
3.2 x1012 N
6 m

 8.0 x10
19
(1.6 x10 C )(2.5T )
s
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!

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.
Sample Problem (not in book)
Fmagnetic  qvB  (1.6 x10


19
m
C )(6 x10 )(3.0T )
s
6
F= 2.88 x 10-12 N
Direction? Use the RHR

V points west, B points out of the page…

F points SOUTH (remember it’s an electron!!)