8 | Electricity
IB Physics Content Guide
- • Electricity consists of charged particles moving in a continuous circuit
- • Voltage, Current, and Resistance are related to each other though Ohm’s
- • The total current flowing into a junction must equal the total current
flowing out of that same junction
- • The voltage dropped around a continuous loop traced in a circuit must
equal the voltage provided
- • Resistors can be combined in different ways to produce different results
- • It is possible that the act of taking a measurement will change the
value being measured
- • The resistance of a wire is affected by its thickness, length, and
- • Many applications use a potential divider circuit design to produce a
result when certain conditions are met
- • The voltage that a battery can supply is related to its internal
8.1 – Electrical Current
- I can quantify charge in terms of Coulombs
- I can calculate the charge of a certain # of electrons and the # of electrons for a given charge
- I can describe current in terms of amps and coulombs per second
- I can describe the subatomic properties of a conductor to allow charge to flow
- I can the electron drift speed for a given current and wire
- I can use Kirchhoff’s First Law to analyze the current flowing in an out of a junction
8.2 – Ohm’s Law and Resistance
- I can use Kirchhoff’s Second Law to analyze the current flowing in an out of a junction
- I can qualitatively describe voltage, current, and resistance
- I can mathematically relate voltage, current, and resistance using Ohm’s Law
- I can describe the difference between ohmic and non-ohmic resistors
- I can identify groups of resistors as being connected in series of parallel
- I can calculate the equivalent resistance for resistors connected in series
- I can calculate the equivalent resistance for resistors connected in parallel
- I can quantitatively describe how adding resistors changes the equivalent resistance
8.3 – Circuits
- I can calculate the equivalent resistance for resistors in a combination circuit with series AND parallel
- I can describe how voltage is divided across resistors in series
- I can describe how current is divided across parallel branches in a circuit
- I can use a circuit diagram to calculate V, I, and R for resistors in simple series or parallel circuits
- I can use a circuit diagram to calculate V, I, and R for resistors in a combination circuit
8.4 – Measuring Circuits and Resistivity
- I can explain how a voltmeter or ammeter must be connected in a circuit
- I can identify the resistance required for an ideal voltmeter or ammeter
- I can predict the reading on a meter when given its internal resistance
- I can calculate a meter’s internal resistance from a meter reading and circuit diagram
- I can calculate the electrical power of a component when given voltage, current, or resistance
- I can qualitatively describe the factors that affect a wire’s resistance
- I can define the resistivity of a meter with proper units
- I can calculate for an unknown variable in the resistivity formula
8.5 – Voltage Dividers and Batteries
- I can identify the different circuit diagram symbols for different types of resistors
- I can describe how environmental changes can affect the resistance of LDRs and Thermistors
- I can describe how changing resistor values can affect the voltage drop experienced
- I can design a potential divider circuit to perform a certain task
- I can compare the differences between primary and secondary cells
- I can describe the mechanics required to recharge a battery
- I can define the electromotive force and describe how is it is different than the battery’s voltage
- I can solve for a circuit that includes a battery with internal resistance
- I can describe how a battery’s voltage changes over time
8 | Electricity
Charge Of 1 Electron
1.6 × 10-19 C
# of Electrons per Coulomb
6.25 × 1018 e–
Cross Sectional Area:
The rate at which charges move through a wire
How hard it is for a current to
flow through a conductor
The total current coming into a junction must equal the
The sum of the voltages (potential differences)
R = 0 Ω
R = ∞ Ω
Ammeters must be connected in series
Voltmeters must be connected in parallel
Cross Sectional Area:
Switch turns on in the dark:
Switch turns on in a fire:
Cannot be recharged
Can be recharged by passing a current through the battery in
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.
- 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 forceCoulomb’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.
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.
ELECTRIC CHARGES AND FIELDS
- Positive charge
- Negative charge
i.e., the sum of positive charges is equal to the sum of negative charges.
CONDUCTORS AND INSULATORS
METHODS OF CHARGING
- By friction : By rubbing two suitable bodies, given in box one is charged by +ve and another by –ve charge in equal amount.
- By conduction : Charging a neutral body by touching it with a charged body is called charging by conduction.
- By induction : Charging a body without bringing it in contact with a charged body is called charging by induction.
PROPERTIES OF ELECTRIC CHARGE
- Similar charges repel and dissimilar charges attract each other.
- A charged body attracts light uncharged bodies, due to polarisation of uncharged body.
- Charge is conserved i.e., the charge can neither be created nor be destroyed but it may simply be transferred from one body to the other.
- Charge is unaffected by motion
This is also called charge invariance with motion
- Quantisation of charge – A charge is an aggregate of small unit of charges, each unit being known as fundamental or elementary charge which is equal to e = 1.6 × 10–19 C. This principle states that charge on any body exists as integral multiple of electronic charge. i.e. q = ne where n is an integer.
charges becomes 1/K times when placed in a medium of
dielectric constant K.
- Polar dielectric
- Non-polar dielectric
DIFFERENCE BETWEEN ELECTROSTATIC FORCE AND GRAVITATIONAL FORCE
VECTOR FORM OF COULOMB’S LAW
SUPERPOSITION PRINCIPLE FOR DISCRETE CHARGE DISTRIBUTION: FORCE BETWEEN MULTIPLE CHARGES
FORCE FOR CONTINUOUS CHARGE DISTRIBUTION
TYPES OF CHARGE DISTRIBUTION
- Volume charge distribution : If a charge, Q is uniformly distributed through a volume V, the charge per unit volume ρ (volume charge density) is defined by
- Surface charge distribution : If a charge Q is uniformly distributed on a surface of area A, the surface charge density , is defined by the following equation
- Linear charge distribution : If a charge q is uniformly distributed along a line of length λ, the linear charge density λ, is defined by
- Fix the origin of the coordinate system on charge q.
- Draw the forces on q due to the surrounding charges considering one charge at a time.
- Resolve the force in x and y-axis respectively and find and
- The resultant force is and the direction is given byand the direction is given by
CALCULATION OF ELECTRIC FORCE IN SOME SITUATIONS
- Force on one charge due to two other charges
- Force due to linear charge distribution
- When the distance between the two charges placed in vacuum or a medium is increased K-times then the force between them decreases K2-times. i.e., if F0 and F be the initial and final forces between them, then
- When the distance between the two charges placed in vacuum or a medium is decreased K-times then the force between them increases K2-times. i.e., if Fo and F be the initial and final forces then F = K2Fo
- When a medium of dielectric constant K is placed between the two charges then the force between them decreases by K-times. i.e., if Fo and F be the forces in vacuum and the medium respectively, then
- When a medium of dielectric constant K between the charges is replaced by another medium of dielectric constant K’ then the force decreases or increases by (K/K’) times according as K’ is greater than K or K’ is less than K.
ELECTRIC LINES OF FORCE
- The lines of force diverge out from a positive charge and converge at a negative charge. i.e. the lines of force are always directed from higher to lower potential.
- The electric lines of force contract length wise indicating unlike charges attract each other and expand laterally indicating like charges repel each other.
- The number of lines that originate from or terminate on a charge is proportional to the magnitude of charge.
- Two electric lines of force never intersect each other.
- They begin from positive charge and end on negative charge i.e., they do not make closed loop (while magnetic field lines form closed loop).
- Where the electric lines of force are
- close together, the field is strong (see fig.1)
- far apart, the field is weak (see fig.2)
- Electric lines of force generate or terminate at charges /surfaces at right angles.
ELECTRIC FIELD FOR CONTINUOUS CHARGE DISTRIBUTION
CALCULATION OF ELECTRIC FIELD INTENSITY FOR A DISTRIBUTION OF DIRECT AND CONTINUOUS CHARGE
- Fix origin of the coordinate system where electric field intensity is to be found.
- Draw the direction of electric field intensity due to the surrounding charges considering one charge at a time.
- Resolve the electric field intensity in x and y-axis respectively and find ΣEx and ΣEy
- The resultant intensity is and where θ is the angle between and x-axis.
- To find the force acting on the charge placed at the origin, the formula F = qE is used.
Energy in unit volume of electric field is called energy density and is given by
ELECTRIC FIELD DUE TO VARIOUS CHARGE DISTRIBUTION
- Electric Field due to an isolated point charge
- A circular ring of radius R with uniformly distributed charge
- A circular disc of radius R with uniformly distributed charge with surface charge density σ
- An infinite sheet of uniformly distributed charges with surface charge density σ
- A finite length of charge with linear charge density
- Due to a spherical shell of uniformly distributed charges with surface charge density σ
- Due to a solid non conducting sphere of uniformly distributed charges with charge density ρ
- Due to a solid non-conducting cylinder with linear charge density λ
- If the electric lines of force are parallel and equally spaced, the field is uniform.
- If E0 and E be the electric field intensity at a point due to a point charge or a charge distribution in vacuum and in a medium of dielectric constant K then
- If E and E’ be the electric field intensity at a point in the two media having dielectric constant K and K’ then
- The electric field intensity at a point due to a ring with uniform charge distribution doesn’t depend upon the radius of the ring if the distance between the point and the centre of the ring is much greater than the radius of the ring. The ring simply behaves as a point charge.
- The electric field intensity inside a hollow sphere is zero but has a finite value at the surface and outside it (; x being the distance of the point from the centre of the sphere).
- The electric field intensity at a point outside a hollow sphere (or spherical shell) does not depend upon the radius of the sphere. It just behaves as a point charge.
- The electric field intensity at the centre of a non-conducting solid sphere with uniform charge distribution is zero. At other points inside it, the electric field varies directly with the distance from the centre (i.e. E ∝ x; x being the distance of the point from the centre). On the surface, it is constant but varies inversely with the square of the distance from the centre (i.e.). Note that the field doesn’t depend on the radius of the sphere for a point outside it. It simply behaves as a point charge.
- The electric field intensity at a point on the axis of non-conducting solid cylinder is zero. It varies directly with the distance from the axis inside it (i.e. E ∝ x). On the surface, it is constant and varies inversely with the distance from the axis for a point outside it (i.e. ).
MOTION OF A CHARGED PARTICLE IN AN ELECTRIC FIELD
- The velocity of the charged particle at time t is,
- Distance travelled by particle is
- Kinetic energy gained by particle,
- the particle will leave the field at a distance from its original path in the direction of field, given by
- The particle will leave the region in the direction of the tangent drawn to the parabola at the point of escape.
- The velocity of the particle at the point of escape is given b
- The direction of the particle in which it leaves the field is given by
ELECTRIC FIELD DUE TO AN ELECTRIC DIPOLE
- Along the axial line (or end-on position)
- Along equatorial line (or broadside on position)
- At any point (from the dipole)
ELECTRIC FORCE BETWEEN TWO DIPOLES
- The dipole moment of a dipole has a direction from the negative charge to the positive charge.
- If the separation between the charges of the dipole is increased (or decreased) K-times, the dipole moment increases (or decreases) by K-times.
- The torque experienced by a dipole placed in a uniform electric field has value always lying between zero and pE, where p is the dipole moment and E, the uniform electric field. It varies directly with the separation between the charges of the dipole.
- The work done in rotating a dipole in a uniform electric field varies from zero (minimum) to 2pE (maximum). Also, it varies directly with the separation between the charges of the dipole.
- The potential energy of the dipole in a uniform electric field always lies between +pE and –pE.
- The electric field intensity at a point due to an electric dipole varies inversely with the cube of the distance of the point from its centre if the distance is much greater than the length of the dipole.
- The electric field at a point due to a small dipole in end-on position is double of its value in broad side-on position,
- For a small dipole, the electric field tends from infinity at a point very close to the axis of the dipole to zero at a point at infinity.
- The force between two dipoles increases (or decreases) by K4-times as the distance between them decreases (or increases) by K-times.
- Time period of a dipole in uniform electric field is
- The electric flux is a scalar although it is a product of two vectors and (because it is a scalar product of the two).
- The electric flux has values lying between –EA and +EA, where E and A are the electric field and the area of cross-section of the surface.
- The net electric flux through any closed surface depends only on the charge inside that surface. In the figures, the net flux through S is q1/εo, the net flux through S’ is (q2 +q3 )/εo and the net flux, through S” is zero.
- The net flux across surface A is zero
APPLICATIONS OF GAUSS’S LAW
- To determine electric field due to a point charge
Gaussian surface and is parallel to (direction normal to Gaussian surface) at every point on the Gaussian surface.
- To determine electric field due to a cylindrically symmetric charge distribution
- The closed imaginary surfaces drawn around a charge are called Gaussian surfaces.
- If the flux emerging out of a Gaussian surface is zero then it is not necessary that the intensity of electric field is zero.
- In the Gauss’s law,
- The net flux of the electric field through a closed surface due to all the charges lying inside or outside the surface is equal to the flux due to the charges only enclosed by the surface.
- The electric flux through any closed surface does not depend on the dimensions of the surface but it depends only on the net charge enclosed by the surface.