Electric Charge

Electrically neutral – most objects have equal amounts of protons & electrons & therefore no net charge

An intrinsic characteristic of a fundamental particle, electrons & protons that accompanies it wherever they exist

Proton = positive Electron = negativeEach has the same value of charge

Electrically charged objects•an object with excess protons will have a positive charge•an object with excess electrons will have a negative charge

Melectron = 9.11x10-31 kgMproton = 1.67x10-27 kg

• Fix the next few slides…check notes

Conductors & Insulators

intermediate between conductors & insulators. Silicon are germanium are examples & these have been used to revolutionize electronics.

Semiconductors:

– giving the charge on an object a free pathway to the Earth. (which is so large it can absorb an infinite amount of charge & remain electrically neutral) Known as discharging an object. It is easier to do to conductors than insulators

Grounding (not what happens when you get busted)

Conservation of charge states that the net sum of total charge in the universe cannot change.

Just like with other conservation laws, charge is exchanged between the objects

In the production of charged particles, equal amount of positive & negative charges are always produced (ex: when an electron is created, a positron is also created – same mass but opposite charge; when a proton is created, an anti-proton is also created, & so on – the same when charged particles are destroyed & turned into energy)

Charge is Conserved

Induction – bringing a charged object near a neutral object. The charges in the neutral object will separate, making one end act as a positive charge & the other end as a negative charge.

Methods of Charging an object

Friction – rubbing two neutral objects together giving them equal amounts of opposite charges

Contact – touching a neutral object with a charged object giving each object the same sign charge & the total charge on the two objects will add up to the original charge (but does not always split evenly)

Polarization

Involves the separation of charge, it is not a method of charge.

Electrostatic Photocopier

Coulomb’s Law states that the electrostatic force between two object is proportional to the product of the forces & inversely proportional to the square of the distance between them.

k is Coulomb’s constant

Coulomb’s Law

Unit of charge:

Charge is not continuous, but made up of multiples of the elementary charge which is that found on an electron or proton

e = 1.6x10-19 Cq = ne

,...3,2,1 n

When a physical quantity can only have discrete values instead of any value, we say that the quantity is quantized

Charge is Quantized

ExampleImagine 3 charges, separated in an equilateral triangle as shown with L = 2.0 cm, q = 1.0 nC. What is the magnitude and direction of the force felt by the upper charge?

The charges and coordinates of two charged particles held fixed in the xy plane are: q1 = +3.0μC, x1 = 3.5cm, y1 = 0.50cm, and q2 = −4.0μC, x2 = −2.0cm, y2 = 1.5cm.

Example2

How far away from q2 should a third charge q3 = +4.0μC be placed such that the net electrostatic force on q2 is zero?

The cause of electric force between charges results from the ELECTRIC FIELD that is established.

ELECTRIC FIELD

ELECTRIC FIELD is a space or region where electric charges experience a electrical force. Each charge creates its own E-field. This is very similar to the g-field that surrounds the Earth.E-FIELD is a VECTOR and is defined as:

E-field Lines This is where the test charge qo comes into play

Based on the diagram, what is the sign of the charge at C and D?

Based on the diagram, what is the charge ratio of C/D?

Typical Electric Fields

The motion of electrons in a radio transmitting antenna creates an electric field. The effect of this electric field can be experienced for many miles around the transmitting antenna. When a radio in the vicinity is tuned to that particular station, the electrons in the receiving antenna experience a force that, with the help of the receiver’s circuits, results in the sounds produced

APPLICATION

Point charges q1 =8.0nC and q2 = -5.0nC are on the x-axis located at x = -5.0 cm and x = 5.0 cm.

Find the NET electric field at a point on the y-axis, 10.0cm above x=0.

Example

Example 2 Two point charges of +3.6uC and -8.7uC are located 3.5m apart. Determine the position where the E-field would be zero other than infinity.

Conceptually, where along the axis would this be possible?

a) To the left of q1

b) To the right of q2

c) In between q1 and q2 ?

Example: A charged cork ball is suspended on a light string in the presence of a uniform electric field as shown. The ball is in equilibrium. E = (3.0i + 5.0j) x 10^5 N/C.

a) Draw an FBD for the ballb) Find the sign & magnitude of charge on the

ball.c) Find the tension in the string.

Example: Ring of ChargeA nonconducting ring of radius R lies in the yz-plane and carries a uniformly distributed positive charge Q

a) Determine an expression for the E-field at a point along the x-axis some distance x from origin.

b) Determine the value of x for which Ex is a maximum.

c) Determine the maximum E-field, Ex max.

e) Describe the motion of an electron placed at x = R/2 and released from rest.

d) On the axes, sketch Ex vs x from x = -2R to x = +2R.

Parallel Plate – Uniform E

A negatively charged particle is moving in

the +x-direction when it enters a region with

a uniform electric field pointing in the +x-

direction. Which graph gives its position as a

function of time correctly? (Its initial

position is x = 0 at t = 0.)

Lightning Rods are pointed

Electric Flux

We define the electric flux , of the electric field E, through the surface A, as:

area A

E

A

Electric Flux

Consider a cylinder immersed in a uniform E-field as shown

E

Determine total flux through cylinder.

Consider a positive point charge outside a spherical container. Determine the net flux,Ф, for the sphere.

+q

r

R

If the surface is irregular, we can integrate over the surface by using tiny pieces of area, dA

Gauss’s Law

Carl Friedrich Gauss 1777-1855

Gauss law relates E on a closed surface, any closed surface, to net charge inside the surface. A closed surface encloses a volume of space such that there is an inside and an outside. Interior of a circle is not a closed surface.

Gauss states that you can tell how much charge you have inside the ‘box’ without actually looking inside the ‘box’. One can just look at field lines entering or exiting.

Gauss’ Law is a restatement of Coulomb’s Law (for E-field, kq/r2 )

The Gaussian surface is fictitious but could represent the closed surface of any object.

Consider a point charge, +q, surrounded by a spherical Gaussian surface, a distance r from +q.

We want to see how the enclosed charge is related to the E-field at the surface of our Gaussian surface.

E-field at surface is given by:

Flux through surface is given by:

Gauss’s Law

The total flux within a closed surface …

… is proportional tothe enclosed charge.

It gives us great insight into the electric fields in and on conductors and within voids inside metals.

It doesn’t matter where or how charge is distributed within surface. Gaussian Surface (GS) is an imaginary surface we fit around charge where E is constant to make integration easier (reason for symmetry). If E isn’t going to be constant at all points, then you must use Coulomb’s Law (more difficult) and look all contributions from each charge.

For which of these closed surfaces (a, b, c, d),will the flux of the electric field, produced by thecharge +2q, be zero?

Calculate the flux of the electric field for each of the closed surfaces a, b, c, and d

Surface a, a =Surface b, b =Surface c, c =Surface d, d =

Consider 2 identical point charges, one positive, the other negative.

Surround the charges with a Gaussian surface

What is the net charge enclosed? What is the net flux through the surface?

What is E at the surface?

Applying Gauss’s LawGauss’s law is useful only when the electric field is constant on a given surface

1. Select Gaussian surface Spherical, cylindrical, or planar

2. Setup integral using appropriate surface area 3. Solve for E

Procedure to follow for all cases of high degree of symmetry:

a) Determine outside the conductorE

Example 1: Thin spherical hollow conductor of radius R with uniformly distributed charge +Q residing on all over surface.

b) Determine inside the conductorE

Conductors

Why does E = 0 inside a conductor?

Conductors are full of free electrons, roughly one per cubic Angstrom (1 angstrom = 1x10-10). These are free to move. If E is nonzero in some region, then the electrons in that region ‘feel’ a force (qE) and start to move.

A charge, +q, inside a neutral conducting shell. Find E for r = a, b, & c

r =a:

Sphericalcavity

a

bc

r = b:

c

r = c:

What would E be like inside cavity if we placed the pt charge outside of the uncharged conductor?

Excess charge is deposited on a conductor. An imaginary Gaussian surface is drawn completely inside the conductor as shown. There can be no electric field on the imaginary surface because it is inside the conductor.  By Gauss's Law we must have Qencl = 0. We conclude that all the excess charges must reside on the outer surface of the solid conductor.

G.S.

A section of conductor is removed . How will that change charge distribution?

What happens when we move the inner charge off-center?

Properties of Conductors in electrostatic equilibrium

In a conductor there are large number of electrons free to move.

Any Excess charge placed on a conductor moves to the exterior surface of the conductor where equilibrium is reached.

The electric field inside a conductor (metal) is zero when charges are at rest.

*A conductor shields a cavity within it from external electric Fields but if there is charge within cavity, E can be present.

Electric field lines contact conductor surfaces at right angles. There can be no net horizontal component or charges would move.

A conductor can be charged by contact or induction

Connecting a conductor to ground is referred to as groundingThe ground can accept of give up an unlimited number of electrons

Example: A very long line of charge

Determine E-field at a distance, r, from the line of charge with linear charge density λ.

r

Example: A very long cylindrical insulator has a uniformly distributed +Q per unit length. Find E outside and inside the cylinder. Insulator has radius R.

Inside insulator:

Very large non-conducting sheet of surface charge density, +σ. Find E outside of sheet.

Very large Conducting sheet of surface charge density, +σ. Find E outside of sheet.

A positive charge distribution exists within a nonconducting spherical region of radius a. The volume charge density is NOT uniform but varies with the distance r from the center of the spherical charge distribution, according to ρ = βr for 0 ≤ r ≤ a, where β is a positive constant and ρ = 0 for r > a.

a) Show that total charge Q in the spherical region of radius ‘a’ is βπa4.

b) In terms of β, a, r, and constants, determine the magnitude of the electric field at a point a distance r from the center of the spherical charge distribution for each of the following cases. i) r > a

ii) r = a

iii) 0 < r < a