Download Electromagnetism is one of the four fundamental forces of nature

Chapter 16
LECTURE NOTES
Electromagnetism is one of the four fundamental forces of nature. There are two types of
electric charges which, following Ben Franklin, we call positive and negative. These exert
electric forces on each other. Experimenting with static electricity (caused by charges at rest) we
find: like charges repel (+ repels +, - repels -) and unlike charges attract (+ attracts -).
Today we recognize the smallest unit of electric charge e, is the magnitude of charge on the
electron. Static electricity results when an object has an excess of electrons (and is – charged) or
a deficit of electrons (and is + charged). In gasses and liquids, ions (atoms with too many or too
few electrons) can also move and transfer charges.
Static electricity is much more noticeable on dry, as opposed to humid, days. Water molecules
are polar, with charge unevenly distributed. They can remove excess electrons or donate
electrons to charged objects, causing the charge to leak away.
Materials are divided into categories according to their ability to conduct charge from one place
to another. Insulators (wood, rubber, glass) have few free charge carriers and do not conduct
electricity well. Conductors (metals) have many free electrons that can move through the
material allowing a transfer of charge. Semiconductors (silicon) have intermediate properties.
An object can be charged by conduction or induction. In conduction, the object is touched to an
already charged material that transfers some of charge. In induction, the object is brought near
an already charge material. This results in an unequal charge distribution in the object. Some of
these charges can be removed leaving the object oppositely charged to the previously charged
material.
Coulomb, a century after Newton, examined the electric force exerted by charged bodies and
kQ1Q 2
found what we now call Columb’s Law. F =
along a line joining the center of the
r2
charges.
The force F is in newtons (N) and is attractive or repulsive as we have discussed. r is the
distance in meters (m) between the center of the charges. Q1 and Q2 are the charges, measured in
coulombs (C). k is a constant = 9 x 109 Nm2/C2. We can define k in terms of a more
1
fundamental constant  0, the permitivity of free space: k =
where  0 = 8.85 x 10-12
40
2
2
C /Nm .
The unit of charge is the coulomb(C). The magnitude of the elementary charge e = 1.6 x 10-19C.
Charges produced by friction resulting in static electrical effects are usually 10-6 C (1  C) or
10-9C (1nC).
Note the similarities between Newton’s Law of Universal Gravitation and Coulomb’s Law.
Chapter 16
LECTURE NOTES
+
+
-
Q1
Q2
Example
Q3
Three charges are on a line. Q1 (+4.00  C) is at x = 0.00. Q2 (-2.00  C) is at x = 0.200m, and
Q3 (+5.00  C) is at x = 0.500m.
Find the magnitude direction of the next force exerted on Q2 by the other charges.
Find F21 the force exerted on charge Q2 by charge Q1.
F21 =
kQ 1 Q 2
r2

(9  10 9
Nm 2
C2
)( 4  10  6 C)( 2  10  6 C)
(0.200m) 2
= 1.8N left.
Note: It is wise to ignore the sign of the charges and determine the direction of the force by the
“unlike charges attract” rule.
Similarly, we can find F32, the force Q3 on Q2.
(9  10 9
F23 =
Nm2
C2
)(5.00  10 6 C)( 2  10 6 C)
(0.300m) 2
Q2 is F21 + F23 = 0.8N, left.
= 1.00N, right. Thus, the net force exerted on
Note: If the forces were not on a line, we would need to find their x and y components and
carefully add the force vectors.
Electric Field
Most common forces (pushes and pulls) are contact forces between objects that are touching.
Gravity and electromagnetism seem to exhibit action at a distance; the force is somehow
transmitted between two bodies not in contact.
Two centuries ago, Faraday introduced the idea of an intermediary field to explain this. An
electric charge Q creates an electric field which fills all space. Any other charge q then feels an
electric force due to its interaction with the local electric field.
Let q be a small positive test charge. Then E = F/q is the electric field at any point in space
where q is located and F is the force q feels. The units of E are N/C. Note, by taking q to be
vanishingly small, its influence on the charge whose field we are trying to measure is minimized.
Note: The direction of the electric field is the direction of the force felt by a positive test charge.
Chapter 16
LECTURE NOTES

 F kQq / r 2 kQ
Example: Electric field due to a point charge Q. By Coulomb’s Law E  
 2 .
q
q
r
Note: The direction of E is radially outward from a positive Q and radially inward toward a
negative Q.
+
x
+
Q1
?
Q2
Example: Given two charges
Q1 (+ 2.00  C) at x = 0.00 and Q2 (+5.00  C) at x = 0.500m.
Find the point on the line between the charges where the net electric field is zero. Let this point
have coordinate x.
kQ1
, right.
x2
kQ 2
The electric field at x due to Q2 is E2 =
, left.
(.5  x ) 2
The electric field at x due to Q1 is E1 =
The directions are found by imagining a small positive test charge is at x and using the “like
charges repel, unlike charges attract” rule.
Now, E = 0 = E1 + E2 =
Thus, E = 0 when
kQ1
kQ 2
where we take right as +.

2
x
(.5  x) 2
kQ1
kQ 2
or x = 0.194m.

2
x
(.5  x ) 2
Field Lines
Faraday visualized the electric field by drawing field lines or lines of force. These are arrows
that indicate the direction of the force at some point in space on a small positive test charge.
They are tangent to the field.
The lines can be drawn so that the number of lines leaving a positive Q or entering a negative Q
is proportional to the magnitude of the charges.
Note: The closer the lines are together, the stronger the field in that region.
Note: Between two plates of charge (one + , one -) the lines point from + to -. We can show that
E = constant between the plates, so we draw the lines equally spaced.
Chapter 16
LECTURE NOTES
Electric Fields and Conductors
The electric field inside a good conductor is zero for electrostatics (no motion of charges).
Any net charge on a conductor resides on its surface, not in the material.
The static electric field is always perpendicular to the surface of a conductor.
Note: A positive charge in the open interior of a metal shell induces an equal negative charge to
migrate to the interior surface of the shell. To keep the shell neutral or have no net charge on the
shell material, an equal positive charge distributes itself over the outer surface. From the outside,
the electric field appears as if the shell was not present.
Note: If we place a hollow conductor in an electric field, the field will not penetrate the interior
of the conductor. You are shielded from electrical effects if in a metal cage.