Unit 6

Electric Forces and Electric Fields

· Electric Charge· Conduction and Induction· Electric Force (Coulomb's Law)•Electric field, shielding

1 The Origin of Electricity

The electrical nature of matter is inherentin atomic structure.

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Coulombs—unit for electric charge

Electric ChargeIt has been known since ancient times that when certainmaterials are rubbed together, they develop an attraction foreach other. (This can be seen today when you take clothesout of a dryer)In ancient Greece - people noticed that when thread wasspun over a spindle of amber, the thread was attracted to thespindle.The Greek word for amber was "elektron," hence this forcewas called electric.

Electric ChargeIn the 18th century, American Ben Franklin noticedw hen a rubberrod is rubbed by animal fur, the rod acquires a negative charge,and the animal fur acquires a positive charge.

When a glass rod is rubbed by silk, the rod acquires a positivecharge and the silk obtains a negative charge. Thus, tworubber rods after being charged would repel each other, whilea rubber rod would be attracted to a glass rod.

No new charge is created - instead, it is just separated - thepositive charge acquired by one object is exactly equal inmagnitude and opposite in sign to the charge lost by the otherobject.

1 The Origin of Electricity

In nature, atoms are normallyfound with equal numbers of protonsand electrons, so they are electricallyneutral.

By adding or removing electronsfrom matter it will acquire a netelectric charge with magnitude equalto e times the number of electronsadded or removed, N.

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1 The Origin of Electricity

Example 1 A Lot of Electrons

How many electrons are there in one coulomb of negative charge?

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The Nature of Charge

Like energy and momentum, charge is neither created nordestroyed, it is conserved.

Opposite charges attract and like charges repel.A s a resultnegatively charged electrons are attracted to the positivenucleus.

Despite the great mass difference, the charge on an electronis exactly equal in magnitude to the charge on a proton, andits magnitude is denoted by "e.“

An electron is said to have a charge of -e anda proton a charge of +e.

Measurement of ChargeThe electron was discovered by J.J. Thomson in 1897, and in aseries of experiments between 1909 and 1913, Robert Millikanand his graduate student, Harvey Fletcher, established the valueof the charge, "e," on an electron.

2. Charged Objects and the Electric Force

It is possible to transfer electric charge from one object to another.

The body that loses electrons has an excess of positive charge, whilethe body that gains electrons has an excess of negative charge.

2 Charged Objects and the Electric Force

LAW OF CONSERVATION OF ELECTRIC CHARGE

During any process, the net electric charge of an isolated system remainsconstant (is conserved).

2 Charged Objects and the Electric Force

Like charges repel and unlike charges attract each other.

2 Charged Objects and the Electric Force

1. An atom in its normal (non-ionic) state has nocharge. This is due to the fact that atoms:

A have only neutrons.B have no protons or electrons.C have equal numbers of protons and electrons.D have an equal number of protons and neutrons.

2. What object moves freely within the entire atom?A Electron.B Neutron.C Proton.D Nucleus.

3. An atom is composed of:A a central nucleus that is surrounded by neutrons.B an even distribution of electrons and protons in a spherical shape.C a central nucleus surrounded by electrons.D a central nucleus containing protons and electrons.

3. Conductors and Insulators

Not only can electric charge exist on an object, but it can also movethrough an object.

Substances that readily conduct electric charge are called electricalconductors.

Materials that conduct electric charge poorly are called electricalinsulators.

SolidsSolids are a form of matter whose nuclei form a fixed structure.Nuclei, and their protons and neutrons, are "locked" into position.

Solids are classified as either conductors, insulators orsemiconductors.

In conductors, some electrons are free to move through the solid and are not bound to any specific atom. In insulators, electrons are bound to their atoms, and may move short distances, but much less than the electrons in a conductor. Semiconductors, depending on their situation, act as either conductors or insulators.

4. Charging by Contact and by Induction

Charging by contact.

Charging by conductioninvolves conductors thatare insulated from theground, touching andtransferring the chargebetween them. Theinsulator is necessary toprevent electrons fromleaving or entering thespheres from Earth.

4. Charging by Contact and by Induction

Total Charge = -4Q(identical spheres very far apart)

Question1: If a conductor carrying a net charge of 8Q is brought intocontact with an identical conductor with no net charge,what will be the charge on each conductor after they areseparated?

Question2: Metal sphere A has a charge of -2Q and an identicalmetal sphere B has a charge of -4Q. If they are broughtinto contact with each other and then separated, what isthe final charge on sphere B?

4 Charging by Contact and by Induction

Charging by induction.

4 Charging by Contact and by Induction

The negatively charged rod induces a slight positive surface chargeon the plastic.

Conduction Summary

Through physical contact, a charged object will transfer a portion of its charge to a neutral object. Because of the Conservation of Charge, the amount of charge on the initially charged object will decrease.

For example, a positively charged object will transfer positivecharge to a neutral object, leaving it with a net positive charge.The amount of positive charge on the initial object will decrease.

Similarly, a negatively charged object will transfer negativecharge to a neutral object.

Induction Summary

A charged object will be brought close to a neutral object, but it willnot touch it. The neutral object will be grounded - it will have anelectrical conducting path to ground. The charged object will repelsimilar charges on the neutral object to the ground.

Thus, the neutral object will be left with a charge opposite to theinitially charged object. The initial object will not lose any charge -the extra charge comes from the ground. As long as the ground isdisconnected before the initial object is removed, the neutral objectwill gain charge.

If the ground were left in place, once the initially charged object wasremoved, the neutral object will pass its gained charge back to theground.

1. Sphere A carries a net positive charge, and sphereB is neutral. They are placed near each other on aninsulated table. Sphere B is briefly touched with awire that is grounded. Which statement is correct?

A Sphere B remains neutral.B Sphere B is now positively charged.C Sphere B is now negatively charged.D The charge on sphere B cannot be determinedwithout additional information.

2.If a positively charged rod touches a neutral conducting sphere and is removed, what charge remains on the sphere? What happens to themagnitude of the charge on the rod?A The sphere becomes positive and the rod's net charge stays the same.B The sphere becomes positive and the rod's net charge decreases.C The sphere becomes negative and the rod's net charge stays the same.D The sphere remains neutral and the rod's net charge stays the same.

Demo

Static electric charge:https://www.youtube.com/watch?v=QxZ6AWLpnUw

Van de Graaf generator experiment:https://www.youtube.com/watch?v=ubZuSZYVBng

5. The Electroscope

The electroscopemeasures electrical charge(both sign and magnitude).

The conductor rod isinsulated from the glasscontainer.When the scope is neutral,the leaves hang down todue to their own mass.

Electroscopes can be charged by conduction or induction.

A neutral electroscope will becomenegatively charged when touched bya negatively charged object.Negative electrical charge willdistribute across the electroscopeand the gold leaves will repel, sincethey have the same charge, and likecharges repel.

The bar is moved away and there is now a negative net charge on the scope. Since negative charge moved from the rod to the electroscope, the rod now has less negativecharge (Conservation of Charge).

1. When a negatively charged rod touches the top of aneutral electroscope, the gold leaves separate. What isthe charge on the leaves?

A NegativeB PositiveC Neutral

2. What is the source of the charge that is moved to the gold leaves?

A The charged bar.B The ground.C The glass surrounding the leaves.

Electrical Force:

6. Coulomb’s Law

In the late 18th Century,several physicists (JosephPriestly and John Robison)reasoned (and Robisonmeasured) that the forcebetween two objectsfollowed the same principlesas the gravitational force andthat the force between twocharged objects depends onthe inverse square of thedistance between them

Charles Coulomb published apaper (1785), based on detailedexperiments, that definitivelyproved the above, and that theforce was also proportional tothe size of the charges.He used a torsion balancewhich was based on the sameprinciple as Henry Cavendish'sexperiment that measured thegravitational constant.

Coulomb’s Law

6 Coulomb’s Law

COULOMB’S LAW

The magnitude of the electrostatic force exerted by one point chargeon another point charge is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance betweenthem.

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Coulomb's Law is used to calculate the magnitude of the force.

Each object exerts the same force on the other - except inopposite directions (Newton's third law applies to all forces, not just mechanical ones).

Since electrical force, like all forces, is a vector, you need tospecify the direction of the force magnitude determined byCoulomb's Law.

This is done by looking at the sign of both charges(like charges repel & opposite charges attract).

6 Coulomb’s Law

Example 3 A Model of the Hydrogen Atom

In the Bohr model of the hydrogen atom, the electron is in orbit about thenuclear proton at a radius of 5.29x10-11m. Determine the speed of the electron, assuming the orbit to be circular.

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Electrical Force relationshipto Gravitational Force

Both forces are expressed using a similar mathematicalformula, where the magnitude of the force decreases as 1/r 2.

Electrical force can be attractive or repulsive (like chargesrepel, opposite charges attract). Gravitational force is always attractive.

The electrical force is on the order of 1036 times stronger than the gravitational force!

2.A +20.0 μC point charge is located 20.0 cm away from a-40.0 μC point charge. What is the force on each due tothe other?

3.What is the distance between two charges +7.8 μC and+9.2 μC if they exert a force of 4.5 mN on each other?

4.A -4.2 μC charge exerts an attractive force of 1.8 mNon a second charge which is a distance of 2.4 m away.What is the magnitude and sign of the second charge?

5.Two equal negatively charged objects repel each other with a force of 18 mN. What is the charge on each object if the distance between them is 9 cm?How many extra electrons are on each object?

6 Coulomb’s Law

Example 4 Three Charges on a Line

Determine the magnitude and direction of the net force on q1.

6 Coulomb’s Law

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Superimposition ofElectrical Forces

Follow this procedure:

1. Assume all charges, other than the one that the initial netforce is being calculated for, are immobile - this will allow thedetermination of the direction of the individual initial forces.

2. Draw a free body diagram for each charge, using the fact thatopposite charges attract and like charges repel.

3. Use Coulomb's Law to find the magnitude of each force.

4. Sum the forces, taking into account that they are vectors withdirection and magnitudes. Use the free body diagrams to assignsigns to the forces - if they point to the right, they are positive; if theypoint to the left, they are negative.

7. The Electric Field

The positive charge experiences a force which is the vector sum of the forces exerted by the charges on the rod and the two spheres.

This test charge should have a small magnitude so it doesn’t affect the other charge.

The Electric Field

Example 6 A Test Charge

The positive test charge has a magnitude of 3.0x10-8C and experiences a force of 6.0x10-8N.

(a) Find the force per coulomb that the test chargeexperiences.

(b) Predict the force that a charge of +12x10-8Cwould experience if it replaced the test charge.

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The Electric Field

DEFINITION OF ELECRIC FIELD

The electric field that exists at a point is the electrostatic force experiencedby a small test charge placed at that point divided by the charge itself:

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SI Units of Electric Field: newton per coulomb (N/C)

7 The Electric Field

It is the surrounding charges that create the electric field at a given point.

The Electric Field

Example 7 An Electric Field Leads to a Force

The charges on the two metal spheres and the ebonite rod create an electricfield at the spot indicated. The field has a magnitude of 2.0 N/C. Determinethe force on the charges in (a) and (b)

The Electric Field

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The Electric Field

Electric fields from different sourcesadd as vectors.

The Electric Field

Example 10 The Electric Field of a Point Charge

The isolated point charge of q=+15μC isin a vacuum. The test charge is 0.20m to the right and has a charge qo=+15μC.

Determine the electric field at point P.

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The Electric Field

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The Electric Field

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The Electric Field

Example 11 The Electric Fields from Separate Charges May Cancel

Two positive point charges, q1=+16μC and q2=+4.0μC are separated in avacuum by a distance of 3.0m. Find the spot on the line between the chargeswhere the net electric field is zero.

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The Electric Field

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The Electric Field

THE PARALLEL PLATE CAPACITOR

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8. Electric Field Lines

Electric field lines or lines of force provide a map of the electric fieldin the space surrounding electric charges.

8. Electric Field Lines

Electric field lines are always directed away from positive charges andtoward negative charges.

8 Electric Field Lines

Electric field lines always begin on a positive chargeand end on a negative charge and do not stop in midspace.

8 Electric Field Lines

The number of lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge.

8 Electric Field Lines

9 The Electric Field Inside a Conductor: Shielding

At equilibrium under electrostatic conditions, any excess charge resides on the surface of a conductor.

At equilibrium under electrostatic conditions, theelectric field is zero at any point within a conductingmaterial.

The conductor shields any charge within it from electric fields created outside the conductor.

9 The Electric Field Inside a Conductor: Shielding

The electric field just outside the surface of a conductor is perpendicular to the surface at equilibrium under electrostatic conditions.

9 The Electric Field Inside a Conductor: Shielding

Conceptual Example 14 A Conductor in an Electric Field

A charge is suspended at the center ofa hollow, electrically neutral, spherical conductor. Show that this charge induces

(a) a charge of –q on the interior surface and

(b) a charge of +q on the exterior surface of the conductor.