Lecture 9

Coulomb’s law

Electric field

3.3 Coulomb’s Law

Coulomb’s law gives the force between two point charges:

The force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if the charges are like.

Coulomb’s law (force between 2 point charges) : 1 212 2

ˆq q

kr

F r

9 2 29.0 10 /k N m C

[q] = Coulomb = C

2 7 2 210 /k c N m C

82.99792458 10c

12 4 , 3 mr ˆ ˆ4 3 m i j

12 16 9 5r m m

9 1 212 212

9 105

q qF F

Example 1: Force Between Two Charges

A 1.0 C charge is at x = 1.0 cm, & a 1.5 C charge is at x = 3.0 cm. What force does the positive charge exert on the negative one? How would the force change if the distance between the charges tripled?(C=10-6 C)

1 212 2

ˆk q q

rF r

9 2 2 6 6

2

9.0 10 / 1.0 10 1.5 10ˆ

0.020

Nm C C C

m

i ˆ34 N i

Distance tripled force drops by 1/32. 12

34 ˆ ˆ3.89

N N F i i

Example 2:

The electron and proton of a hydrogen atom are separated (on the average) by a distance of approximately . Find the magnitudes of the electric force between the two particles?

115.3 10 m

Example 3:

Consider three point charges located at the corners of a right triangle as shown in this Figure, where q1= q3= 5.0 μC, q2 = -2.0 μC, and a = 0.10 m. Find the resultant force exerted on q3.?

3.4.1 The Electric Field

Definition of the electric field:

Here, q0 is a “test charge” – it serves to allow the electric force to be measured, but is not large enough to create a significant force on any other charges.

The electric field of a point charge points radially away from a positive charge and towards a negative one.

Just as electric forces can be superposed, electric fields can as well.

3.3.2 Electric Field Lines

Electric field lines are a convenient way of visualizing the electric field.

Electric field lines:

1. Point in the direction of the field vector at every point

2. Start at positive charges or infinity

3. End at negative charges or infinity

4. Are more dense where the field is stronger

The charge on the right is twice the magnitude of the charge on the left (and opposite in sign), so there are twice as many field lines, and they point towards the charge rather than away from it.

Combinations of charges. Note that, while the lines are less dense where the field is weaker, the field is not necessarily zero where there are no lines. In fact, there is only one point within the figures below where the field is zero – can you find it?

A parallel-plate capacitor consists of two conducting plates with equal and opposite charges. Here is the electric field:

If we know the electric field, we can calculate the force on any charge:

The direction of the force depends on the sign of the charge – in the direction of the field for a positive charge, opposite to it for a negative one.

Example 4:

A charge q1 = 7.0 μC is located at the origin, and a second charge q2 = -5.0 μC is located on the x axis, 0.30 m from the origin (see this Figure). Find the electric field at the point P, which has coordinates (0, 0.40) m.