# electrostatics

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Electrostatics: Forces

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Concept Check - Electrostatics
Two charged balls are repelling each other as they hang from the
ceiling. What can you say about their charges?

1. one is positive, the other is negative
2. both are positive
3. both are negative
4. both are positive or both are negative
Concept Check - Electrostatics
Two charged balls are repelling each other as they hang from the
ceiling. What can you say about their charges?

1. one is positive, the other is negative
2. both are positive
3. both are negative
4. both are positive or both are negative

The fact that the balls repel each other only can tell you that they
have the same charge, but you do not know the sign. So they can
be either both positive or both negative.
Concept Check - Electrostatics
From the picture, what can you conclude about the charges?

1.           have opposite charges

2.           have the same charge

3.              all have the same charge

4. one ball must be neutral (no charge)
Concept Check - Electrostatics
From the picture, what can you conclude about the charges?

1.           have opposite charges

2.           have the same charge

3.              all have the same charge

4. one ball must be neutral (no charge)

The PERIWINKLE and BLACK balls must have the same charge,
since they repel each other. The RED ball also repels the
PERIWINKLE , so it must also have the same charge as the
PERIWINKLE (and the BLACK).
Concept Checks – Conductors
A metal ball hangs from the ceiling by an insulating thread. The ball is
attracted to a positive-charged rod held near the ball. The charge of
the ball must be:

1.   positive
2.   negative
3.   neutral
4.   positive or neutral
5.   negative or neutral
Concept Checks – Conductors
A metal ball hangs from the ceiling by an insulating thread. The ball is
attracted to a positive-charged rod held near the ball. The charge of
the ball must be:

1.   positive
2.   negative
3.   neutral
4.   positive or neutral                                         remember
the ball is a
5.   negative or neutral
conductor!
Clearly, the ball will be attracted if its charge is negative.
However, even if the ball is neutral, the charges in the ball can be
separated by induction (polarization), leading to a net attraction.
Concept Checks – Conductors (2)
Two neutral conductors are connected by a wire and a charged rod is
brought near, but does not touch. The wire is taken away, and then the
charged rod is removed. What are the charges on the conductors?

1.       0        0                                    0      0
2.       +        –

3.       –        +

4.       +        +

5.       –        –
?      ?
Concept Checks – Conductors (2)
Two neutral conductors are connected by a wire and a charged rod is
brought near, but does not touch. The wire is taken away, and then the
charged rod is removed. What are the charges on the conductors?

1.       0        0                                     0      0
2.       +        –

3.       –        +

4.       +        +

5.       –        –
?      ?
While the conductors are connected, positive charge will flow from the
blue to the green ball due to polarization. Once disconnected, the
charges will remain on the separate conductors even when the rod is
removed.
Concept Check – Charging by Induction
A positively charged object is placed close to a conducting object
attached to an insulating glass pedestal (a). After the opposite side of
the conductor is grounded for a short time interval (b), the conductor
becomes negatively charged (c). Based on this information, we can
conclude that within the conductor

1. both positive and negative charges move freely.
2. only negative charges move freely.
3. only positive charges move freely.
4. We can’t really conclude anything.
Concept Check – Charging by Induction
A positively charged object is placed close to a conducting object
attached to an insulating glass pedestal (a). After the opposite side of
the conductor is grounded for a short time interval (b), the conductor
becomes negatively charged (c). Based on this information, we can
conclude that within the conductor

1. both positive and negative charges move freely.
2. only negative charges move freely.
3. only positive charges move freely.
4. We can’t really conclude anything.
Electromagnetic Charge
Positive and Negative Charge
Positive
(+)

Air        Rubber balloon

Human Hands        Sulphur

Asbestos       Hard rubber

Rabbit's Fur   Nickel, Copper

Glass        Brass, Silver

Human Hair     Gold, Platinum

Mica            Sulfur

Nylon       Acetate, Rayon

Wool          Polyester

Cat's Fur     Polyurethane

Silk        Polyethylene

Aluminum      Polypropylene

Paper            Vinyl

Cotton           Silicon

Steel           Teflon

Wood         Saran Wrap
Negative
Lucite           (-)

Sealing wax
Amber
Polystyrene
Polyethylene
Insulators and Conductors

+                   + +
+
+                   +           + + ++
+               + + + ++
+                            + +
+                           +
+               + ++
+       +
+                       +   +
+
+                   +
+

Conductor           Nonconductor
Insulators and Conductors

+
+         +
+   +
+            +
+   + +
+            +
+ +
+        +
+
Q
+                    +
+ +      +       +   + +      +       +
+   +                +   +
+                    +
+                    +

+                                                                    +
+ +           +       +                                               + +      +       +
Q/2                                                                   Q/2
+       +                                                            +   +
+                                                                    +           +
+
Concept Check – Coulomb’s Law
What is the magnitude of the force F2?

1.   1.0 N               F1 = 3N             F2 = ?
Q     Q
2.   1.5 N
3.   2.0 N
4.   3.0 N
5.   6.0 N
Concept Check – Coulomb’s Law
What is the magnitude of the force F2?

1.   1.0 N               F1 = 3N                F2 = ?
Q        Q
2.   1.5 N
3.   2.0 N
4.   3.0 N
5.   6.0 N

The force F2 must have the same magnitude as F1. This is due to
the fact that the form of Coulomb’s Law is totally symmetric with
respect to the two charges involved. The force of one on the other
of a pair is the same as the reverse. Note that this sounds
suspiciously like Newton’s 3rd Law!!
Concept Check – Electric Force
Two uniformly charged spheres are firmly fastened to and electrically
insulated from frictionless pucks on an air table. The charge on sphere
2 is three times the charge on sphere 1. Which force diagram correctly
shows the magnitude and direction of the electrostatic forces:
Concept Check – Electric Force
Two uniformly charged spheres are firmly fastened to and electrically
insulated from frictionless pucks on an air table. The charge on sphere
2 is three times the charge on sphere 1. Which force diagram correctly
shows the magnitude and direction of the electrostatic forces:
Concept Check – Coulomb’s Law (2)
If we increase one charge to 4Q, what is the magnitude of F1?
F1 = 3N                     F2 = ?
1.   3/4 N                                        Q             Q
2.   3.0 N
3.   12 N                               F1 = ?                      F2 = ?
4.   16 N                                         4Q            Q
5.   48 N
Concept Check – Coulomb’s Law (2)
If we increase one charge to 4Q, what is the magnitude of F1?
F1 = 3N                     F2 = ?
1.   3/4 N                                        Q             Q
2.   3.0 N
3.   12 N                               F1 = ?                      F2 = ?
4.   16 N                                         4Q            Q
5.   48 N
q1q2
Originally we had: F1  K 2  3N
r
Now we have: F1  K
 4q1  q2  4K q1q2 =4F =12N
1
r2            r2
which is 4 times bigger than before.
Concept Check – Coulomb’s Law (3)
The force between two charges separated by a distance r is F. If the
charges are pulled apart to a distance 3r, what is the force on each
charge?
F                       F
1. 9 F                              Q            Q
2. 3 F
3. F                                       r
4. 1/3 F           ?                                              ?
5. 1/9 F                Q                                     Q

3r
Concept Check – Coulomb’s Law (3)
The force between two charges separated by a distance r is F. If the
charges are pulled apart to a distance 3r, what is the force on each
charge?
F                       F
1. 9 F                              Q            Q
2. 3 F
3. F                                       r
4. 1/3 F           F/9                                            F/9
5. 1/9 F                Q                                     Q

3r
q1q2
Originally we had: F  K 2
r
qq       qq 1
Now we have: F     K 1 22  K 1 22 = F
 3r     9r    9
which is 1/9 as big as before.
Concept Check – Coulomb’s Law (4)
A hydrogen atom is composed of a nucleus containing a single proton,
about which a single electron orbits. The electric force between the two
particles is 2.3 x 1039 greater than the gravitational force! If we can
adjust the distance between the two particles, can we find a separation
at which the electric and gravitational forces are equal?

1. Yes, we must move the particles farther apart.
2. Yes, we must move the particles closer together.
3. No, at any distance
Concept Check – Coulomb’s Law (4)
A hydrogen atom is composed of a nucleus containing a single proton,
about which a single electron orbits. The electric force between the two
particles is 2.3 x 1039 greater than the gravitational force! If we can
adjust the distance between the two particles, can we find a separation
at which the electric and gravitational forces are equal?

1. Yes, we must move the particles farther apart.
2. Yes, we must move the particles closer together.
3. No, at any distance

Both the electric and gravitational forces vary as the inverse square of
the separation between two bodies. Thus, the forces cannot be equal at
any distance.
Concept Check – Electric Force
Two balls with charges +Q and +4Q are fixed at a separation distance
of 3R. Is it possible to place another charged ball Q0 on the line
between the two charges such that the net force on Q0 will be zero?

1.   yes, but only if Q0 is positive
2.   yes, but only if Q0 is negative
3.   yes, independent of the sign (or value) of Q0
4.   no, the net force can never be zero                       +4Q
+Q

3R
Concept Check – Electric Force
Two balls with charges +Q and +4Q are fixed at a separation distance
of 3R. Is it possible to place another charged ball Q0 on the line
between the two charges such that the net force on Q0 will be zero?

1.   yes, but only if Q0 is positive
2.   yes, but only if Q0 is negative
3.   yes, independent of the sign (or value) of Q0
4.   no, the net force can never be zero                       +4Q
+Q

3R

A positive charge would be repelled by both charges, so a point
where these two repulsive forces cancel can be found. A negative
charge would be attracted by both, and the same argument holds.
Concept Check – Electric Force (2)
Two balls with charges +Q and +4Q are separated by 3R. Where
should you place another charged ball Q0 on the line between the two
charges such that the net force on Q0 will be zero?
+4Q
+Q
1       2       3       4      5

R              2R

3R
Concept Check – Electric Force (2)
Two balls with charges +Q and +4Q are separated by 3R. Where
should you place another charged ball Q0 on the line between the two
charges such that the net force on Q0 will be zero?
+4Q
+Q
1       2       3       4      5

R              2R

3R
q0q
The force on Q0 due to +Q is: F  K 2
r
q  4q  4 q  q 
The force on Q0 due to +4Q is:  F K 0 2  K 0 2 F
 2r   4   r 
Since +4Q is 4 times bigger than +Q, then Q0 needs to be farther
from +4Q. In fact, Q0 must be twice as far from +4Q, since the
distance is squared in Coulomb’s Law.
Coulomb’s Law

1
FE 
r

FE  q1q2

q1q2
FE  2
r
q1q2
FE  ko 2       where ko  8.98755179 10 9 N  m 2 C 2
r
Coulomb’s Law

F12           F32

q1 (+)               q2 (-)                         q3 (+)

F2  F21  F23

F13                F13
q3 (+)

F23                     F23
F3
q1 (+)                         q2 (-)

Concept Check – Forces in 2D
Which of the arrows best represents the             1
direction of the net force on charge +Q                     2
3
due to the other two charges?
4
d
+2Q       +Q               5
d

+4Q
Concept Check – Forces in 2D
Which of the arrows best represents the             1
direction of the net force on charge +Q                     2
3
due to the other two charges?
4
d
+2Q       +Q               5
d

+4Q
The charge +2Q repels +Q
towards the right. The
charge +4Q repels +Q
upwards, but with a stronger
force. Therefore, the net
force is up and to the right,            +2Q
but mostly up.

+4Q
Concept Check – Electric Force (3)
Two balls with charges +Q and –4Q are fixed at a separation distance
of 3R. Is it possible to place another charged ball Q0 anywhere on the
line such that the net force on Q0 will be zero?

+Q                    – 4Q

1.   yes, but only if Q0 is positive                 3R
2.   yes, but only if Q0 is negative
3.   yes, independent of the sign (or value) of Q0
4.   no, the net force can never be zero
Concept Check – Electric Force (3)
Two balls with charges +Q and –4Q are fixed at a separation distance
of 3R. Is it possible to place another charged ball Q0 anywhere on the
line such that the net force on Q0 will be zero?

+Q                       – 4Q

1.   yes, but only if Q0 is positive               3R
2.   yes, but only if Q0 is negative
3.   yes, independent of the sign (or value) of Q0
4.   no, the net force can never be zero

A charge (positive or negative) can be placed to the left of the +Q
charge, such that the repulsive force from the +Q charge cancels
the attractive force from –4Q.
Electric Field

F
E
qo

F qE

F      q qo 1
E     ko 2
qo      r qo

q
E  ko         Field of a Point-charge
r2
Concept Check – Electric Fields
Consider the four field patterns shown. Assuming there are no charges
in the regions shown, which of the patterns represent(s) a possible
electrostatic field:

1. (a)
2. (b)
3. (b) and (d)
4. (a) and (c)
5. (b) and (c)
6. some other combination
7. None of the above.
Concept Check – Electric Fields
Consider the four field patterns shown. Assuming there are no charges
in the regions shown, which of the patterns represent(s) a possible
electrostatic field:

1. (a)
2. (b)
3. (b) and (d)
4. (a) and (c)
5. (b) and (c)
6. some other combination
7. None of the above.
Concept Check – Electric Fields (2)
An electrically neutral dipole is placed in an external field. In which
situation(s) is the net force on the dipole zero?

1. (a)
2. (c)
3. (b) and (d)
4. (a) and (c)
5. (c) and (d)
6. some other combination
7. none of the above
Concept Check – Electric Fields (2)
An electrically neutral dipole is placed in an external field. In which
situation(s) is the net force on the dipole zero?

1. (a)
2. (c)
3. (b) and (d)
4. (a) and (c)
5. (c) and (d)
6. some other combination
7. none of the above
Electric Fields

Electrostatics Java Applet   Electric Fields in 2D   Electric Fields in 3D
Superposition of Fields
Electric Fields
Electric Fields Web Resources

Electric Field Simulation

More Electric Field Examples

Field Lines Applet

CalTech E-field Java Applet
Electric Field of a Point-Charge
Electric Field of a Dipole
Electric Field of Parallel Plates
Electric Fields and a Conductor

E=0
Concept Check – Force of Electric Field
In a uniform electric field in empty space, a 4 C charge is placed and it
feels an electrical force of 12 N. If this charge is removed and a 6 C
charge is placed at that point instead, what force will it feel?

1.   12 N
2.   8N
3.   24 N                          Q
4.   no force
5.   18 N
Concept Check – Force of Electric Field
In a uniform electric field in empty space, a 4 C charge is placed and it
feels an electrical force of 12 N. If this charge is removed and a 6 C
charge is placed at that point instead, what force will it feel?

1.   12 N
2.   8N
3.   24 N                          Q
4.   no force
5.   18 N

Since the 4 C charge feels a force, there must be an electric field
present, with magnitude: E = F / q = 12 N / 4 C = 3 N/C
Once the 4 C charge is replaced with a 6 C charge, this new
charge will feel a force of: F = q E = (6 C)(3 N/C) = 18 N
Concept Check – Electric Fields
What are the signs of the charges whose electric fields are shown at
right?
1)

2)

3)

4)

5) no way to tell
Concept Check – Electric Fields
What are the signs of the charges whose electric fields are shown at
right?
1)

2)

3)

4)

5) no way to tell

Which has a greater magnitude of charge?

```
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