Topic 6.2 Electric Force and Field (3 hours)

Electric Charge There are two types of electric charge, positive charge and negative charge. It was not until the late 1890s through the work of J.J. Thomson that the true nature of electrons was discovered through experiments with cathode ray tubes. We now know that charge is conserved charge is quantised the force between two point charges varies as the inverse square law of the distance between the two charges.

Electrostatics: The study of stationary charges. Unlike protons which are strongly bound in the nucleus, the electrons in a material are relatively free to move, and some electrons, given the right conditions, can move from one material to another. The materials can become electrically charged. Materials can either have an excess of electrons or a deficiency of electrons. substances with an excess of electrons are negatively charged. substances with a deficiency of electrons are positively charged.

When a perspex rod is rubbed with a piece of silk, the perspex rod becomes positively charged and the silk becomes negatively charged as demonstrated in the figure.

Law of Conservation of Charge When charging objects by friction, charge is not created but rather redistributed on the two surfaces. This can be stated according to the Law of Conservation of Electric Charge that states that in a closed system, the amount of charge is constant. If you examine the previous figure more closely – there is a total of 16 positive charges and a total of 16 negative charges on the perspex rod and the silk before rubbing. After the process of “ electrification ” by friction, the charge is redistributed but the same number of positive and negative charges exist. In other words, charge is conserved.

Electrostatic Force Like charges repel each other Unlike charges attract each other

Measuring Charge The coulomb (symbol: C) is the SI derived unit of electric charge. It is defined as the charge transported by a steady current of one ampere in one second. 1 C = 1 A ∙ s The elementary charge, usually denoted as e, is the electric charge carried by a single proton, or equivalently, the absolute value of the electric charge carried by a single electron. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called the elementary positive charge. This charge has a measured value of approximately 1.602 × 10−19 C. Conversely, one coulomb is the charge carried by 6.25 × 1018 electrons or protons.

Conductors Metals consist of positive ions surrounded by a ‘sea’ of delocalized electrons (electrons that are not all attached to a specific atom). Hence there are many electrons available for conduction. Solutions that conduct (electrolytes) contain electrons and positive and negative ions that are free to move. Therefore, conductors have a low electrical resistance.

If a conductor is held in the hand, any excess of electron charge that forms on the conductor will be transferred to the earth through the body of the person holding the conductor. Conversely, any deficiency of electron charge that forms on the conductor will be transferred from the earth through the body of the person holding the conductor. It is said that the conductor is earthed or grounded.

Insulators In an insulator, the electrons are held tightly by the atomic nuclei and are not as free to move through a material. They can accumulate on the surface of the insulator but they are not conducting.

Band Gap Theory According to the energy band theory that is used to explain the properties of conductors, semiconductors (such as germanium and silicon), and insulators, the valence or outer-shell electrons are held in the valence band that is full or partially filled with electrons. When there are many atoms in close proximity (as there is with all materials), there also exists an upper energy band known as the conduction band. The conduction band is empty. A forbidden energy gap exists between the valence and conduction bands.

For conductors such as metals, the valence and conduction bands overlap. However, in insulators, the energy gap between the valence band and the conduction band is large. Therefore, electrons cannot move across the forbidden energy gap. Insulators thus have a high electrical resistance and when an insulating material is held, the electrons remain on the surface of the insulator and are not able to be conducted through the person. The charge on an insulator will remain for a short period of time until it leaks off the surface or is discharged.

The Electroscope http://www.shep.net/resources/curricular/physics/p30/unit2/electroscope.html

Coulomb’s Law The French physicist, Charles Augustin Coulomb (1738‑1806), using a torsion balance of his own invention, confirmed the existence of an inverse square law of electric charge.

Coulomb’s Law On the basis of his experiments, he concluded that the force F between two point charges q1 and q2 was directly proportional to the product of the two point charges. the force between the two point charges was inversely proportional to the square of the distance between them r2. Together this gives:

Coulomb’s Law When F is measured in newtons (N), q1 and q2 in coulombs (C), and r in metres (m), the quantitative statement of k is the constant of proportionality called the Coulomb Constant. Its value is 8.99 × 109 N m2 C-2. Note that it is not necessary to include the sign of the charge when carrying out the calculations. Simply use the magnitude of the point charges and then draw a diagram with the signs of each point charge shown, this will also indicate whether the force is attractive or repulsive.

Alternate Coulomb’s Law You may also see Coulomb’s Law written as where k is replaced by 1 / 4πε0. The part of the constant ε0 is called the permittivity constant of free space. On its own, it has a value of 8.95 × 10 -12 N m2 C -2 , and this value applies if the experiment is carried out in air or in a vacuum. If the experiment is carried out in another medium, the value of ε0 will need to be substituted with another value.

Example: Two charges, q1 = 4.00 mC and q2 = 6.00 mC, are placed in a straight line separated by a distance of 2.00 cm as shown below. Find the force exerted on each charge. 1 2

If another charge, q3 = - 2. 5 mC is placed 3 If another charge, q3 = - 2.5 mC is placed 3.00 cm above q2 (as shown below) then what is the net force experienced by q2? 3 1 2

Homework: Tsokos, Pages 287 and 288, Questions 1 to 15

Electric Field Michael Faraday (1791-1867) reasoned that just as Newton had developed the gravitational field concept, so too the concept of electric field could be an analogy of this. Faraday argued that an electric field is a region of influence around a point charge or group of point charges.

Electric Field If an electric field is present at a particular place, when a second point charge is placed near it, it feels a force. The stronger the field, the stronger the electric force will be. The electric field has direction because the force on the charged particle has direction. The direction of the electric field is defined as the direction of the force it causes to act on a small positive test charge.

Electric Field Lines Faraday introduced the concept of electric field lines to show the direction that an isolated charge would follow if placed in the field.

Rules for Electric Field Lines they start on a positive charge and end on a negative charge they meet electrostatically charged objects at right angles they never cross over one another their density is an indication of the strength of the electric field there is no electric field in a hollow conductor the electric field is uniform between two oppositely charged parallel conducting plates.

Electric Fields For Some Common Charge Distributions

Electric Field Strength The electric field strength or electric field intensity at any point in space, E is equal to the force per unit charge exerted on a positive test charge. Electric field strength is a vector quantity and it is measured in N C -1

Now throw in Coulomb’s Law… and become Where k is Coulomb’s constant, q1 is the point charge producing the electric field, q2 is the small test charge, and r is the distance from q to the particular point in space. (Recall that the units for E are N C-1)

Example: The electric field between two parallel plates is 100.0 N C-1. What acceleration would a charge of 2.0 mC and mass 1.00 x 10-3kg experience if placed in this field. (Ignore its weight)

Charges and Potential Energy Consider a fixed positive charge Q and a positive test charge q that is infinitely far away from Q. If the test charge q is moved close to Q, work must be done to overcome the repulsive force between the two charges. Because of the work done to overcome this repulsive force, there is now an equal amount of potential energy stored is this system. Q q q

Electric Potential We define the electric potential (V) at a point as the work per unit charge that must be done to bring a small positive test charge from far away to the point of interest. where V is the potential in volts (1 V = 1 J/C), W is the work done (in J) which equals the potential energy, and q is the magnitude of the test charge (in C).

Electric Potential Difference Now consider an arrangement of charges that creates an electric potential in the space around it. Suppose you now move a charge from one potential to another, the work that must be done is given by or

Energy in Electronvolts The relationship W = qDV allows us to define a new unit of energy, the electronvolt. One electron volt is the work done when one elementary charge (e) is taken across a potential difference of 1 V. NOTE: 1 C∙V = 1 J

Example: A charge of 5.0 mC and mass of 2.0 x 10-8 kg is shot with a speed of 300. m/s between two parallel plates kept at a potential of 200. V and 300. V respectively. What speed will the charge have when it reaches the 300. V plate?

Two parallel plates have a potential difference between them of 250 V Two parallel plates have a potential difference between them of 250 V. What work must be done to move a charge of 5.0 mC from the negative (low) plate to the positive (high) plate.

What is the speed of a proton whose kinetic energy is 5000. eV?

Homework Tsokos, Pages 296 to 298, Questions 1 to 15