A glass rod is charged positive by rubbing it with (artificial) fur. It is then used to charge the electroscope as follows: the rod is brought near to the electroscope terminal, causing a deflection. While the rod is held in place, a grounded wire is touched to its terminal, discharging the electroscope. The glass rod is then withdrawn, resulting in a deflection of the electroscope.

That same glass rod is then charged positive in the same way and brought near to the terminal of the electroscope. How will the electroscope respond? When the charged glass rod is brought near the terminal, the electroscope will: (a) indicate a higher voltage.

(b) indicate a lower voltage.(c) remain the same.(b) indicate a lower voltage.

How do charges interact?

• If you have two charges of any sign placed close to each other and isolated from the rest of the universe, what could happen?

• Charges could push each other away – Repulsive Force• One charges could pull the other towards itself – Attractive Force

These are not contact forces!

Attractive and Repulsive Forces

Repulsive Repulsive

Attractive Attractive

Are each of the following attractive or repulsive forces?

Three pithballs are suspended from thin threads. Various objects are then rubbed against other objects (nylon against silk, glass against polyester, etc.) and each of the pithballs is charged by touching them with one of these objects. It is found that pithballs 1 and 2 repel each other and that pithballs 2 and 3 repel each other. From this we can conclude that

1. 1 and 3 carry charges of opposite sign.2. 1 and 3 carry charges of equal sign.3. all three carry the charges of the same sign.4. one of the objects carries no charge.5. we need to do more experiments to determinethe sign of the charges.

Three pithballs are suspended from thin threads. Various objects are then rubbed against other objects (nylon against silk, glass against polyester, etc.) and each of the pithballs is charged by touching them with one of these objects. It is found that pithballs 1 and 2 attract each other and that pithballs 2 and 3 repel each other. From this we can conclude that

1. 1 and 3 carry charges of opposite sign.2. 1 and 3 carry charges of equal sign.3. all three carry the charges of the same sign.4. one of the objects carries no charge.5. we need to do more experiments to determine the sign of the charges.

Determination of the magnitude of attractive or repulsive forces between point charges

1q

2q

= magnitude of first point charge

= magnitude of second point charge

r12 = separation distance between q1 and q2

ke = Proportionality constant = 8.99 x 109

= Magnitude of electric force that q1 exerts on q2

e0 = Permittivity of free space = 8.85 x 10-12

0

1

4ek

2

2

Nm

C

2

2

C

Nm

1 212 2

12

ek q qF

r

Coulomb’s Law

12F

Permittivity -

•How easily charge flows through free space

•Different materials have their own permittivity

Point charge – charged object with negligible dimensions

Determination of direction of attractive or repulsive forces

q1q2

q1 q2

F21 F12

F21 F12

F21 = -F12

F21 = -F12

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 greaterthan 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

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:

Example: Two charges, one positive and one negative are separated by a distance of 2 cm. The positive charge has a magnitude of 2 C and the negative charge has a magnitude of 2 C

a) What is the magnitude and direction of the force on charge 2 by charge 1?

b) What is the magnitude and direction of the force on charge 1 by charge 2?

c) What happens to the magnitude and direction of the answer from a) if the positive charge is doubled?

d) What happens to the magnitude and direction of the answer from b) if the negative charge is doubled?

2 cm

q1q2

2 cm

q1q2

F12F21

212

2112 r

qqkF e

c) If q1 is doubled to 4 C the magnitude of the force is also doubled to 1.80 x 1014 N, but the direction doesn’t change

221

2121 r

qqkF e

a) = 8.99 x 1013 N towards q1

b) = 8.99 x 1013 N towards q2

d) If q2 is doubled to 4 C the magnitude of the force is also doubled to 1.80 x 1014 N, but the direction doesn’t change

This is an example of Newton’s 3rd Law!!!

Interactions between more than two charges

• Forces are vectors and must be combined using vector addition.

• You will typically examine the net force on one of the charges present.

q1 q2q3r12 r23

F12

F32

F2 = F12 + F32 1 212 2

12

ˆek q qF r

r

1 2

12 312

ek q qF r

r

Vector form of Coulomb’s Law