Week 1 - S2 Feb. 15 – 20, 2016 Fields 4.1.Electric Fields 4.2. Magnetic Fields Teacher: Mohammad Mezaael

4.1.Electric Fields 4.1.1 state that electric fields are created by electric charges; 4.1.2 define electric field strength as force per unit positive charge;
 4.1.3 select and use the equation E = F/q 4.1.4 select and use the equation for Coulomb's law: F= Qq/( 4 πε0 r2) 4.1.5 select and use the equation for the electric field strength of a point charge: E=Q/(4πε0 r2)
 4.1.6 state that a uniform electric field exists between oppositely charged parallel plates:
 4.1.7 select and use the equation for field strength between charged parallel plates: E = V/d ;
 4.1.8 sketch the electric field lines and equi-potentials for a point charge, a spherically symmetric charge distribution, the region between two parallel plates and an electric dipole;


parallel plate capacitor microfarad coulomb electric field capacitance Vocabulary Terms charge electrically neutral static electricity positive charge negative charge electric forces charge by friction electroscope protons neutrons electrons gravitational field charged induction Coulomb’s law capacitor parallel plate capacitor microfarad coulomb electric field capacitance charge polarization shielding test farad field inverse square law discharged field lines

Unit of charge is a Coulomb (C) Electric Charge Fundamental Charge: The charge on one electron. e = 1.6 x 10 -19 C Unit of charge is a Coulomb (C) Two types of charge: Positive Charge: A shortage of electrons. Negative Charge: An excess of electrons. Conservation of charge – The net charge of a closed system remains constant.

A quantity of charge should always be identified with a positive or a negative sign.

Number of electrons > Number of protons -2e = -3.2 x 10-19C Nucleus - - + n - n + + n n + n - + + n - - - Negative Atom Number of electrons > Number of protons -2e = -3.2 x 10-19C Neutral Atom Number of electrons = Number of protons Positive Atom Number of electrons < Number of protons +2e = +3.2 x 10-19C

Electric Forces Electric forces are created between all electric charges. Because there are two kinds of charge (positive and negative) the electrical force between charges can attract or repel. Like Charges - Repel + F Unlike Charges - Attract - + F

Electric Field Space around a charge What is the difference?

The electric field is the space around an electrical charge just like a gravitational field is the space around a mass.

The electric field strength, E , is the force, Felec, per unit charge, q, at a point. The equation for EFS is (arrows show the units for each symbol) E = Felec q

E = F/ qo qo , positive test charge E is a vector quantity Unit: N/C E is analogous to the gravitational field, g, where g=F/m

Example 1: If the electric field strength due to some charged object is 1.5E3 N/C, find the force on a positive charge due to 2E-4 C placed in the field. Known: E = 1.5E3 N/C & q = 2E-4 C Unknown = Felec Equation: E = Felec / q (solve for Felec)

Felec = (1.5E3 N/C) x (2E-4 C) = 0.30 N If the charge on the object in example #1 was doubled, does that change the electric field strength? Hint: what change would increasing q have on Felec?

Increasing q will increase Felec so ratio between the two is constant. Conclusion = size of test charge doesn’t effect “E”

Coulomb’s Law Coulomb’s Law: the electric force is directly proportional to the product of their charges and inversely proportional to the square of the distance between their charges. Felec = K x q1x q2 d2

The force between two charges gets stronger as the charges move closer together. The force also gets stronger if the amount of charge becomes larger.

Electric Field Strength for a Point Charge Consider the force felt by a charge q in the field of another charge Q, where the charges are separated by a distance r. F = kQq / r2 But E = F/q, so E = k Q / r2 The electric field strength for a point charge Q is inversely proportional to the square of the distance from the point charge. +Q +q F r

Example 1: Work out the field strengths at the points labelled A and B in the diagram below. What do you notice about the values, and why is this? Add arrows at A and B to indicate the electric field strengths there. 10 cm -5C 20 cm B A EA = kQ/r2 = -1.124 x 1012 N C-1 EB = kQ/r2 = -4.5 x 1012 N C-1 (attractive force).

Electric Field Strength Between Charged Parallel Plates For a given separation and p.d, the electric field strength between two parallel plates is constant (uniform field), except at the edges. A point charge q is moved between the plates and experiences a constant force F due to the uniform electric field. Work done on the charge = energy transformed by the charge Fd = Vq Rearranging this equation, we have F / q = V / d By definition, F/q = E, so E = V / d E is directly proportional to the p.d (or V) between the two plates and inversely proportional to the separation of the plates (d). Units of electric field strength are V m-1 or N C-1 + + + + + + ++ + + + + + + + - E = V/d +q d

Two parallel conductors

Example 2: A charged dust particle is stationary between two horizontal charged metal plates. The metal plates have a separation of 3.6 cm and the p.d between the plates is 720 V. The dust particle has a charge of +7e, where e = 1.6 x 10-19 C. Calculate: (a) The electric field strength between the plates b) The weight of the dust particle Solution: a) E = V / d = 720 / 0.036 = 2.0 x 104 V m-1 b) The particle is stationary, therefore the net force must be zero. Weight = Electric force = Eq = 2.0 x 104 x (7 x 1.6 x 10-19) = 2.2 x 10-14 N

Facts Increasing the amount of charge will increase the electric force. (Why ?) Increasing the distance between the charges will decrease the electric force (Why ?) Felec is + if the 2 charges are alike (similar) indicating that they will repel each other (Why ?) Felec is – if the 2 charges are different indicating that they will attract each other (Why ?)

Example 3: Two 40 gram masses each with a charge of 3μC are placed 50cm apart. Compare the gravitational force between the two masses to the electric force between the two masses. (Ignore the force of the earth on the two masses). 3μC 40g 50cm

The electric force is much greater than the gravitational force

To summarise Gravitational Fields Electrical Fields A gravitational field exists in a region of space in which a stationary mass experiences a force. An electric field exists in a region of space in which a stationary charge experiences a force. Gravitational field strength is the force per unit mass on a point mass placed at that point. g = F / m Electric field strength is the force per unit positive charge on a point charge placed at that point. E = F / Q F = Gm1m2/r2 Inverse Square Law F = kQ1Q2/r2 F is attractive only F is attractive or repulsive g = Gm/r2 For the field strength due to a point mass E = kQ/r2 For the field strength due to a point charge

F1 and F2 must be added together as vectors. Example 4 Three charged objects are placed as shown. Find the net force on the object with the charge of -4μC. - 5μC 20cm 45º F1 5μC - 4μC F2 F1 and F2 must be added together as vectors.

+ F1 = < - 4.5 , 0.0 > F2 = < 1.6 , - 1.6 > 2.3cos45≈1.6 - 2.9 F2 45º 29º θ - 1.6 3.31 2.3sin45≈1.6 F1 = < - 4.5 , 0.0 > + F2 = < 1.6 , - 1.6 > Fnet = < - 2.9 , - 1.6 > 3.31N at 209º

Example 5 Two 8 grams, equally charged balls are suspended on earth as shown in the diagram below. Find the charge on each ball. q 20º L = 30cm FE 10º 30sin10º r =2(30sin10º)=10.4cm r

Draw a force diagram for one charge and treat as an equilibrium problem. Tsin80º FE 80º Fg = .08N Tcos80º

Electric Potential Energy charges also have electrical potential energy +Q d +Q v

Electric Potential Energy Work done (by electric field) on charged particle is QEd Particle has gained Kinetic Energy (QEd) Particle must therefore have lost Potential Energy U=-QEd

Electric Potential The electric potential energy depends on the charge present We can define the electric potential V which does not depend on charge by using a “test” charge Change in potential is change in potential energy for a test charge per unit charge for uniform field

Electric Potential compare with the Electric Field and Coulomb Force If we know the potential field this allows us to calculate changes in potential energy for any charge introduced

Electric Potential Electric Potential is a scalar field it is defined everywhere it doesn’t depend on a charge being there but it does not have any direction

Electric Potential, units SI Units of Electric Potential Units are J/C Alternatively called Volts (V) We have seen Thus E also has units of V/m

Potential in Uniform field +Q C d|| +Q +Q A B

Electric Potential of a single charge Advanced E B +

Capacitors A system of two conductors, each carrying equal charge is known as a capacitor

Capacitance of charged sphere - definition r= +Q potential due to isolated charge R

Capacitors e.g. 2: two parallel sheets e.g. 1: two metal spheres +Q -Q Each conductor is called a plate

Equi-potential Lines Like elevation, potential can be displayed as contours Like elevation, potential requires a zero point, potential V=0 at r= Like slope & elevation we can obtain the Electric Field from the potential field A contour diagram

Electric field lines around a positive point charge are directed radially outward.  The reason is the fact that test charge is defined as a small positive charge.  When test charges are placed around a positive charge, they will be repelled and move radially outward.  On the contrary, when test charges are placed around a negative charge, they will be pulled radially inward.  The field lines for a single positive and a single negative point charge when each acts alone are shown in the following figure:  

Equipotential surfaces are necessarily spheres centered at the point charge.  At any point on an equipotential surface (or sphere around a single point charge), the potential is the same.  That is the reason for the choice of word “equipotential.”  field lines are always perpendicular to equipotential lines. This concept may be used to draw field lines around any type of charge distribution if equipotential lines are first determined.

The field lines and equipotential lines around an electric dipole are shown below:

The field lines and equipotential lines around a charge distribution similar to that of a parallel-plate capacitor are shown below: