Electric Charge and Electric Charge and Electric FieldElectric Field

ELECTRIC CHARGES & ELECTRIC FIELDS

*Properties of electric charges

*Coulomb’s law

*Electric field

*Electric field of continuous charge distribution

*Electric field lines

*Motion of charged particles in a uniform electric field

Learning Outcomes

• On the completion of this chapter students should be able to:

• Draw, explain, write the strength and determine the electric field around a charged particle and a configuration of charged particle and the electric forces experienced by or exerted upon any charged particle or any configuration of charged particles.

Static Electricity; Electric Charge and Its Conservation

Objects can be charged by rubbing – posses net electric charge

Ex – combing your hair , touched a metal doorknob after sliding the carpet

(a) Rub a plastic ruler and (b) bring it close to some tiny pieces of paper.

Static Electricity; Electric Charge and Its

Conservation

• Benjamin Franklin(1706-1790)

• Positive charge – possessed by protons

• Negative charge – possessed by electrons

• Charges of same sign repel• Charges of opposite signs

attract

(a)A negatively charged rubber rod suspended by a thread is attracted to a positively charged glass rod.

(b) A negatively charged rubber rod is repelled by another negatively charged rubber rod.

Electric Charge in the Atom

Atom:

Nucleus (small, massive, positive charge)

Electron cloud (large, very low density, negative charge)

Electric Charge in the Atom

Atom is electrically neutral.

Rubbing charges objects by moving electrons from one to the other.

Electric Charge in the Atom

Polar molecule: neutral overall, but charge not evenly distributed

Diagram of a water molecule. Because it has opposite charges on different ends, it is called a “polar” molecule.

Conductor:

Charge flows freely

Metals

Insulator:

Almost no charge flows

Most other materials

Some materials are semiconductors.

Insulators and Conductors

(a) A charged metal sphere and a neutral metal sphere.

(b) (b) The two spheres connected by a conductor (a metal nail), which conducts charge from one sphere to the other.

(c) (c) The two spheres connected by an insulator (wood); almost no charge is conducted.

Induced Charge

Metal objects can be charged by conduction:

A neutral metal rod in (a) will acquire a positive charge if placed in contact (b) with a positively charged metal object. (Electrons move as shown by the orange arrow.) This is called charging by conduction.

- +ve charged metal is brought close to uncharged object-If the 2 object touch, free e- in neutral are attracted to +ve charged and pass over to it. - so,nuetral metal rod now will miss –ve e and will have net +ve charge

Charging a metallic object by induction (that is, the two objects never touch each other).

(a) A neutral metallic sphere, with equal numbers of positive and negative charges.

(b) The electrons on the neutral sphere are redistributed when a charged rubber rod is placed near the sphere.

(c) When the sphere is grounded, some of its electrons leave through the ground wire.

(d) When the ground connection is removed, the sphere has excess positive charge that is nonuniformly distributed.

(e) When the rod is removed, the remaining electrons redistribute uniformly and there is a net uniform distribution of positive charge on the sphere.

They can also be charged by induction, either while connected to ground or not:

Induced Charge

Charging by induction.Inducing a charge on an object connected to ground.

They can also be charged by induction, either while connected to ground or not:

Induced Charge

Charging by induction.Inducing a charge on an object connected to ground.

• both object do not touch•Free electron of metal rod do not leave the rod- they will move within the metal toward the external +ve charged and leaving charged at opposite end•So, charged is induced at the 2 end of metal rod

Induced Charge

Nonconductors won’t become charged by conduction or induction, but will experience charge separation:

The electroscope can be used for detecting charge.

Induced Charge; the Electroscope

Coulomb’s Law

Experiment shows that the electric force between two charges is proportional to the product of the charges and inversely proportional to the distance between them.

Experiment shows that the electric force between two charges is proportional to the product of the charges and inversely proportional to the distance between them.

Coulomb’s Law

Coulomb’s law, Eq. 21–1, gives the force between two point charges, Q1 and Q2, a distance r apart.

Properties of electric force between two stationary charge particles: The electric force..

• is inversely proportional to square of the separation between particles and directed along the line joining them

• is proportional to the product of the charges q1 and q2 on the two particles

• is attractive if charges are of opposite sign and repulsive if the charges are of the same sign

• Is a conservative force

Coulomb’s Law equation

• An equation giving the magnitude of electric force between two point charges

• (Point charges defined as a particle of zero size that carries an electric charge)

221

eer

qqkF

Where ke is called the Coulomb constant and

ke = 8.9875 x 109 Nm2C-2 (S.I units) or

ke = 1/ 4πЄ0 and

Є0 = permittivity of free space

= 8.8542 x 10-12 C2N-1m-2

Coulomb’s law:

This equation gives the magnitude of the force between two charges.

Coulomb’s Law

Coulomb’s LawThe force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if they are the same.

The direction of the static electric force one point charge exerts on another is always along the line joining the two charges, and depends on whether the charges have the same sign as in (a) and (b), or opposite signs (c).

Coulomb’s Law

Unit of charge: coulomb, C

The proportionality constant in Coulomb’s law is then:

Charges produced by rubbing are typically around a microcoulomb:

Coulomb’s Law

Electric charge is quantized in units of the electron charge.

Coulomb’s Law

The proportionality constant k can also be written in terms of , the permittivity of free space:

(16-2)

Two point charges separated by a distance r exert a force on each other that is given by Coulomb’s law. The force F21

exerted by q2 on q1 is equal in magnitude and opposite in direction to the force F12 exerted by q1 on q2. When the charges are of the same sign, the force is repulsive.

Electric Force is a vector

When the charges are of opposite signs, the force is attractive.

rF ˆ2

21e12

r

qqk

Where, is a unit vector directed from q1 to q2.

Since the force obeys Newton’s third law, then

F12 = - F21

r̂

Example: Question 1

• The electron and proton of a hydrogen atom are separated by a distance of approximately 5.3 x 10-11 m. Find the magnitude of the electric force.

Example: Solution 1

221

eer

qqkF

11

2199

e5.3x10

)(1.6x10x8.99x10F

Fe = 8.2 x 10-8 N

Coulomb’s LawExample 2: Three charges in a line.

Three charged particles are arranged in a line, as shown. Calculate the net electrostatic force on particle 3 (the -4.0 μC on the right) due to the other two charges.

Exercise

1. What is the magnitude of the force a +25 µC charge exerts on a +2.5 mC charge 28 cm away?

Exercise

2. Three point charges, Q1 = 3 µC, Q2 = -5 µC, and Q3 = 8 µC are placed on the x-axis as shown in Figure 1. Find the net force on the charge Q2 due to the charges Q1 and Q3.

Q1

20 cm 30 cm

Q2 Q3

Exercise

3. Particles of charge +75, +48 and -85 µC are placed in a line . The center one is 0.35 m from each of the others. Calculate the net force on each charge due to the other two.

Coulomb’s LawExample 3: Electric force using vector components.

Calculate the net electrostatic force on charge Q3 shown in the figure due to the charges Q1 and Q2.

Coulomb’s LawApproach

1. We use Coulomb’s law to find the magnitude of the individual forces.

2. The direction of each force will be along the line connecting Q3 to Q1 or Q2.

3. The forces F31 and F32 have the directions shown in figure,

Q1 exerts an attractive force on Q3

Q2 exerts a repulsive force on Q3

4. The forces F31 and F32 are not in the same line, so to find the resultant force on Q3, we resolve F31 and F32 into x and y components and perform vector addition.

Exercise

1. Three charged particles are placed at the corners of an equilateral triangle of side 1.20 m . The charges are +7.0µC, -8.0µC and -6.0µC. Calculate the magnitude and direction of the net force on Q1 due to the other two.

Electrical Force with Other Forces, Example

The spheres are in equilibrium.

Since they are separated, they exert a repulsive force on each other.

– Charges are like charges

Model each sphere as a particle in equilibrium.

Proceed as usual with equilibrium problems, noting one force is an electrical force.

Section 23.3

Electrical Force with Other Forces, Example cont.

The force diagram includes the components of the tension, the electrical force, and the weight.

Solve for |q|

If the charge of the spheres is not given, you cannot determine the sign of q, only that they both have same sign.

Section 23.3

Examples

Two indentical small spheres, each having a mass of 3.00 x 10-2 kg, hang in equilibrium as shown in Figure. The length, L of each string is 0.150m and the θ= 5.000. Find the magnitude of the charge on each sphere.

• Two kinds of electric charge – positive and negative.

• Charge is conserved.

• Charge on electron:

e = 1.602 x 10-19 C.

• Conductors: electrons free to move.

• Insulators: nonconductors.

Summary

• Charge is quantized in units of e.

• Objects can be charged by conduction or induction.

• Coulomb’s law:

Summary