# 5.1 Electric Fields

#### Electric charge (q or Q)

• Property of matter, either positive, + (e.g. protons), negative, - (e.g. electrons) or neutral (e.g. neutrons).

• Opposite charges attract each other, while like charges repel each other.

• Units: Coulombs (C).

• Definition: "1 C is the charge transported by a current of one ampere in one second".

• Elementary/electron charge (e): The basic unit, equal to 1.6 x 10^-19 C.

• Principle of conservation of charge: Total charge is always conserved.

Materials

• Conductors: have many free electrons that act as charge carriers, such as metals.

• Insulators: do not have many free electrons and reduce the current, such as rubber.

Electric force

Coulomb's law: Electric force = KQ1Q2/r^2, where Q1 and Q2 are the bodies' charges, r is the distance between them and k is Coulomb's constant, which is equal to 1/(4πεo); εo is the permittivity of free space (vacuum).

Electric fields

• Electric field: space that surrounds a charge and influences small test charges, which do not disturb the field. No electric field inside a conducting sphere.​

• Electrical field strength: "The electrical field strength is defined as the electric force per unit charge experience by a small positive point/test charge at a given point."

• E = F/q = KQ/r^2, where q is the charge experiencing the field and Q the charge creating the field.

• Units: NC^-1 or Vm^-1.

• Field's lines: show the direction of the force on a small positive test charge, which is the same direction as the electrical field strength (E).​ Always away from + and into -.

• The field is stronger where the lines are more packed together.

• The field lines never touch each other.

Electric current (I)

• Electric current: rate of flow of electrical charge, carried by charge-carriers, such as electrons (e-), also called conduction electrons.

• Direction: Electrons travel in the opposite direction to the field, as they have negative charge.

• Occurrence: It occurs in a conductor only with the presence of an electric field.

• Normally, there is movement of charges in both directions, so it is cancelled and no current flows.

• When the electric field "rises", the current forms itself instantaneously.​

• Direct current: when there is motion of charges in the same (and only one) direction.​

• Positive ions remain static in this process, receiving kinetic energy from the electrons.

• Formula: I = total charge that moved past a point/time taken for this movement = ∆q/∆t.

• Units: Amperes (A). 1 A = 1 C s^-1.

Tip:

"We have to distinguish the conventional current - the flow of positive charge - and the flow of charge-carriers. If protons carry positive charge from A to B, then we have no problem in saying that the current flows from A to B. A gets less positive, B gets more positive. But, if electrons carry negative charge from A to B, clearly the current is in the opposite direction. A is now getting more positive and B less positive. So we have to say that the conventional current is moving from B to A." (Kognity, 2016)

Electric potential (V)

• Definition: "The electric potential of a point is the work per unit charge required to move a small positive test charge". V = W/q.

• Units: Volts (V), 1 V = 1 JC^-1.

• Equipotential lines: Lines in which the potential is equal.

• Perpendicular to the electric field lines.​

• Potential gradient: the distance between equipotential lines is equal to: - electrical field strength = - E = -V/d.

• Electric potential difference (pd/∆V): "The electric potential difference between two points is the work done per unit charge to move a small point charge from one point to the other." It is sometimes called voltage.

• Path: The actual path of a charge does not affect the amount of work done.

• Energy: If a charge move because of the field, it will increase its kinetic energy and decrease its potential energy.

• Electronvolt (eV): ​"Work done to move one electron across a potential difference of one volt." 1 eV = 1.6 x 10^-19 J.

# 5.2 Heating Effect on Electric Currents

The heat in electric cells is caused because of inelastic collisions of electrons with the surrounding atoms, known as lattice atoms, which receive the kinetic energy and vibrate, thus increasing temperature.

Circuit diagram

Electrical Resistance (R)

• Definition: "The potential difference V across a component divided by the current passing through it.". R = V/I.

• Units: Ohms (Ω). 1 Ω = 1 V A^-1

• Ohm's law: "At constant temperature, the voltage across a component is proportional to the current passing through it".

• Graph: Resistance can be determined as V/I in any point of the graph's line.

Non-ohmic components: Components that do not obey Ohm's law.

• Lamp bulb/filament lamp: ohmic at low currents, because high currents cause great temperature increase, causing resistance to rise, and thus, current to decrease.​​

• Semiconducting diodes: only allow flow in one direction.

• Thermistor: as the temperature increases, its resistance falls, as the lattice ions vibrate more and impede charge-carriers movement.

• Resistivity (ρ) = RA/l, where R is the resistance, A is the area and l is the length of the wire.

• Combining resistors:

Electrical Power (P)

Power Work done/Time taken = qV/tIV = RI^2 V^2/R

Potential divider

• Definition: circuit component that changes the voltage according to each specific situations.

• Using sensors: one fixed-value resistor and one sensitive resistor (to external conditions).

• Thermistor: negative temperature coefficient: resistance proportional to 1/temperature.

• Light-dependent resistor (LDR): resistance proportional to 1/light intensity.

• Potentiometer (rheostat): allows a wide range of potential differences, depending on the connection point of the slider, giving a max-value emf, an advantage of series of resistors.

Kirchhoff's circuit laws

• First law: "The sum of the currents/total charge flowing into a junction equals the sum of the currents/total charge flowing away from a junction." ∑I = 0.

• Second law: "In a complete circuit loop, the sum of the voltages equals zero."  ∑∆V = ∑IR = 0.

Measuring devices

• Ammeter: Measures the current of a circuit. In series with the circuit, with ideal zero resistance. Non-ideal ammeters have low constant resistance.

• Voltmeter: Measures the potential difference across a device. In parallel with the circuit, with ideal infinite resistance. Non-ideal voltmeters have high constant resistance.

# 5.3 Electric Cells

Electromotive force (emf/ε): "Total potential difference across a cell's terminals when no current is flowing (I = 0)." ε W/q P/I ∑potential differences in the circuit.

Internal resistance (r): "Resistance of the components/chemicals within the cell itself, leading to energy/power loss in the cell." It is possessed by a real battery. ε = I(R+r).

Terminal potential difference: pd across a real battery's terminals, V = ε - IR.

V-I graph for a real cell:

Cells

• Battery: chemical energy transformed into thermal, mechanical,...energy.

• Primary cell (Non-rechargeable):"cells used until they are exhausted and then discarded".

• Secondary cell (rechargeable):"possibility of the reversion of chemical reactions into original form". e.g. lead-acid cell.

• Recharging process: Return the energy in the reverse current direction at dp above nominal.

• Discharging a cell: "The terminal potential difference of a typical practical electric cell loses its initial value quickly, has a stable and constant value for most of its lifetime, followed by a rapid decrease to zero as the cell discharges completely" (IB Physics Guide, 2014).

# 5.4 Magnetic Effects of Electric Circuits

Magnetic field (B)

• Poles: North (N) and South (S).

• Existence: only if a force acts on a pair of magnetic poles.

• Opposite poles attract each other, while like poles repel each other.

• Electric currents produce magnetic fields, e.g. Earth's molten iron core.

• Magnetic field lines: Always from North-pole to South-pole.

• Right-hand grip rule (for wires): "Grip the wire with the fingers of the right hand in such a way that the thumb points in the direction of the [conventional] current. Then the direction in which the fingers curls is the direction of the 'flow' of the magnetic field vectors". (Tsokos, 2014)

• Representation of current

• Dot: current leaving the page towards you.

• Cross: current entering page away from you.

• Representation of current and magnetic field around it​

• As the lines are further from the wire, the distance between them increases, as the field becomes weaker.

• Solenoid: field runs along its hollow centre and outside it (coil of wire).

Magnetic force on a moving charge

• Equation: F​ =  qvBsinθ, where B is the magnetic field strength, q is the charge's value, v is the speed of the moving charge and θ is the angle its speed has with the magnetic field lines.

• Magnetic field strength (B) definition by charges: "Force acting per unit charge per speed, on a positive moving charge perpendicular to the magnetic field."​

• There is no magnetic force on a moving charge if the charge moves along the field direction.

• Fleming's left-hand rule for positive moving charges (vectorial product): for negative charges, the force is in the opposite direction.

# v

Motion of charges in magnetic fields: no work is done, as force is perpendicular to speed.

• Circular path: When the speed is perpendicular to the magnetic field.​

• Helical path: When the charge enters the field at a certain angle.

Magnetic force on current-carrying wires​​

• Equation: F​ =  BILsinθ, where B is the magnetic field strength, I is the current on the wire and L is the wire's length.

• Magnetic field strength (B) definition by current: "Force acting per unit current in a wire per unit length, which is perpendicular to the field". Unit: tesla (T).

• Fleming's left-hand rule for wires with current: vectorial product.

• Magnetic force between two current-carrying wires: depends on each wire's current direction.

• If currents are in the same direction:​ attract!

• If currents are in opposite directions: repel!

• Magnetic force between a bar magnet and a current: catapult field.