ELECTROSTATICS II - Form 3 Physics Notes

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Charge Distribution on the Surface of a Conductor

  • The quantity of charge per unit area of the surface of a conductor is called charge density.
  • The charge distribution on a conductor depends on the shape of the conductor.
  • Generally, the charge concentration on a spherical conductor is uniform while that on a sharp point is high.
    charge distribution
  • The high charge concentration at sharp points makes it easier to gain or lose charges.
  • The effects of high charge concentration at sharp points can be seen in the following cases:

Electric Wind

  • When a highly charged sharp point is brought close to a candle flame, the flame is observed to drift away as if there was wind.
  • The high charge concentration at the sharp point ionizes the surrounding air producing both positive and negative charges.
  • Opposite charges are attracted to the point while similar charges are repelled away from the point blowing away the flame.
    electric wind 1
  • If the point is brought very close, the flame splits into two; one part moves towards the point and the other part away from the point.
  • This is because a flame has both positive and negative ions.
  • The negative ions are attracted towards the point while the positive ions are repelled away from the point.
    electric wind 2

Lightning Arrestors

  • When clouds move in the atmosphere, they rub against the air particles and produce a large amount of static charges by friction.
  • These charges induce large amounts of the opposite charge on the earth.
  • Hence a high potential difference is created between the earth and cloud.
  • This makes air to be a charge conductor.
  • The opposite charges attract each other and neutralize, causing thunder and lightning.
  • Lightning can be very destructive to buildings and other structures.
  • Lightning arrestors are used to safeguard such structures.
  • It consists of a thick copper plate buried deep under the ground.
  • The plate is connected by a thick copper wire to the spikes at the top of the building.
    lightning arrestor1
  • The arrestor assumes the same charge as the earth. At the spikes, a high charge density builds up and a strong electric field develops between the cloud and the spikes.
  • The air around the spikes is ionized. The opposite charges attract each other and neutralize. Excess electrons flow to the ground through the thick copper wire.
  • It is for this reason that people are advised not to take shelter under trees when it is raining.

Applications of Static Charges

Electrostatic Precipitator

  • One of the causes of air pollution globally is increased industrialization.
  • Some industries have indeed responded to this challenge by installing electrostatic precipitators which are found within the chimneys.
  • An electrostatic precipitator consists of a cylindrical metal plate fixed along the walls of the chimney and a wire mesh suspended through the middle.
  • The plate is charged positively by connecting it to a high voltage, approximately 50,000V and the wire mesh charged negatively.
  • As a result, a strong electric field exists between the plate and the wire mesh.
  • The ionized pollutant particles get attracted; some to the plate and others to the wire mesh.
  • The deposits are removed occasionally. The same principle is used in fingerprinting and photocopying.
    electrostatic precipitator

Spray Painting

  • The nozzle of the spraying can is charged. When spraying, the paint droplets acquire similar charge and spread out finely due to repulsion.
  • As the droplets approach a metallic body, they induce opposite charge which then attracts them to the metal surface. This ensures that little paint is used.

Dangers of Static Charges

  • When a liquid flows through a pipe, its molecules rub against each other and against the walls of the pipe and become charged.
  • If the liquid is flammable like petrol, it is likely to cause sparks or even explosion.
  • This can also happen to fuels when they are packed in plastic containers.
  • It is therefore advisable to store fuels and other flammable liquids in metallic containers so that any charges generated can continually leak out.
  • This also explains why long chains hang underneath fuel tankers as they move.

Electric Field

  • This is the region around a charged body where its influence (attraction and repulsion) can be felt.
  • It is represented lines of force called electric field lines.
  • The direction of an electric field is the direction in which a positive charge would move if placed at that point.
  • Electric field lines have the following properties:
    • Originate from a positive charge and terminate at a negative charge
    • Do not cross each other i.e. do not intersect
    •  Are parallel at uniform field, close together at strong fields and widely spaced at weaker fields.

Electric Field Patterns

  • The electric field pattern between two charged bodies obeys the law of electrostatics.
  • Below are some patterns between charged bodies:
    electric field patterns
    NB: At the neutral point, the resultant effect is zero.


  • A capacitor is a device used for storing charge.
  • It consists of two or more metal plates separated by a vacuum or a material medium (insulator). This material is known as a ‘dielectric’.
  • Other materials that can be used as a dielectric include air, plastic, glass e.t.c. the symbol of a capacitor is shown below:
  • There are three main types of capacitors namely
    • Paper capacitors,
    • Electrolytic capacitors and
    • Variable capacitors.
  • Others include plastic, ceramic and mica capacitors.

Charging a Capacitor

Experiment: To Charge a Capacitor

Apparatus : Uncharged capacitor of 500μF, 5.0V power supply, rheostat, voltmeter, milliammeter, switch, connecting wires and a stop watch.
charging a capacitor circuit


  1. Set up the apparatus as shown above.
  2. Close the switch and record the values of current, I at various time intervals. Tabulate your values in the table below:
     Time, t(s)  0  10  20  30  40  50  60  70
     Current, I(mA)                
     It (mAs)                
  3. Plot a graph of current, I against time, t
  4. Plot a graph of It against time.


  • The charging current is initially high but gradually reduces to zero. A graph of current, I against time appears as shown below:
    graph of current agaisnt time Charging of a capacitor
  • The charging current drops to zero when the capacitor is fully charged. As the p.d. across the capacitor increases the charge in the capacitor also increases up to a certain value.
  • When the capacitor is fully charged, the p.d across the capacitor will be equals the p.d of the source.
  • A graph of p.d across the capacitor against time is exponential. A graph of It against time is also exponential.
    charging a capacitor graph
    NB The product It represents the amount of charge in the capacitor.

Discharging a Capacitor

Experiment: To Discharge a Capacitor

Apparatus : A charged capacitor, resistor, galvanometer, switch and connecting wires.
discharging a capacitor circuit

  1. Set up the apparatus as shown above.
  2. Close the switch and record the values of current at various time intervals in the table below.
     Time, t(s)  0  10  20  30  40  50  60  70
     Current, I(mA)                
  3. Plot a graph of current, I against time, t.


  • The value of current is seen to reduce from maximum value to zero when the capacitor is fully discharged.
  • The galvanometer deflects but in the opposite direction to that during charging.
  • During discharging, the p.d. across the capacitor reduces to zero when the capacitor is fully discharged.
  • The graphs below show the variation between current, I and time, t and between the p.d across the capacitor and time, t.
  • A graph of charge in the capacitor, Q against time, t during discharging also appears like that of p.d against time i.e. p.d across the capacitor is directly proportional to the charge stored.
    graph between current and time tdischarging a capacitor
    graph of potential difference against timedischarging capacitor


  • Capacitance of a capacitor is defined as the measure of the charge stored by the capacitor per unit voltage;
    C = Q/V
    Hence Q = CV
    Recall: Q = It
    Therefore Q= CV = It
  • The SI Unit of capacitance is the farad, F.
  • A farad is the capacitance of a body if a charge of one coulomb raises its potential by one volt.
  • Other smaller units of capacitance are: microfarad (μF), nanofarad (nF) and picofarad (Pf).
    i.e. 1 μF = 10-6 F
    1 nF = 10-9 F
    1 pF = 10-12 F

Factors Affecting Capacitance of a Capacitor

  • The capacitance of a parallel plate capacitor depends on three factors, namely:
    • Area of overlap of the plates, A
    • Distance of separation, d between the plates
    • Nature of the dielectric material

Experiment: To Investigate the Factors Affecting Capacitance

Apparatus: 2 aluminium plates, K and L of dimensions 25cm * 25cm , Insulating polythene support , uncharged electroscope , Glass plate , earthing wireand a free wire.
factors affecting capcitance experiment


  • Fix the plates on the insulating support so that they stand parallel and close to each other as shown above.
  • Charge plate K to a high voltage and then connect it to the uncharged electroscope. Earth the second plate, L.
  • While keeping the area of overlap, A the same vary the distance of separation, d and observe the leaf divergence.
  • While keeping the distance of separation, d constant vary the area of overlap, A and observe the leaf divergence.
  • While keeping both the area of overlap and the distance of separation, d constant introduce the glass plate between the plates of the capacitor and observe what happens to the leaf.


  • When the distance of separation is increased the leaf divergence also increased.
  • When the area of overlap is increased the leaf divergence decreased.
  • When the glass plate is introduced between the plates, the leaf divergence increased.
    Note that the leaf divergence here is a measure of the potential, V of plate K.
    Hence the larger the divergence the greater the potential and thus the lower the capacitance ( since C = Q/V, but Q is constant).


  • From the above observations, it follows that the capacitance is directly proportional to the area of overlap between the plates and inversely proportional to the distance of separation.
  • It also depends on the nature of the dielectric material.
    C ∝ A/d
    C = εA/d where ε is a constant called permittivity of the dielectric material (epsilon).
  • If between the plates is a vacuum, then ε = εo , known as epsilon nought and is given by 6.85 × 10-12 Fm-1.
    Hence C = εoA/d

Example 4.1

  1. How much charge is stored by a 300μF capacitor charged up to 12V? give your answer in (a) μC (b) C
    (ans 3600μC/0.0036C)
    1. Q= CV = 300×12 =3600μC
    2. 3600 × 10-6 =0.0036C
  2. What is the average current that flows when a 720μF capacitor is charged to 2V in 0.03s?
    (ans 0.24A)
    Q = CV =It
    I= 720 × 10-6 × 2/0.03 =0.24A.
  3. Find the separation distance between two plates if the capacitance between them is 1.0 × 10-12 C and the enclosed area is 5.0 cm2. Take εo = 6.85× 10-12 Fm-1 .
    (ans d = 1.425 × 10-4 m)
    C = εA/d
    d = 6.85 × 10-12 × 5.0 × 10-4/1.0 × 10-12
    = 1.425 × 10-4 m

Arrangement of Capacitors

Series Arrangement

  • Consider three capacitors; C1, C2 and C3 arranged as shown below:
    series arrangement of capacitors
    Recall V = V1 + V2 + V3 and Q = CV
  • When capacitors are connected in series, the charged stored in them is the same and equals the charge in the circuit.
    i.e. Q = Q1 = Q2 =Q3
    Therefore V1 = Q/C1 , V2 = Q/C2 , and V3 = Q/C3
    V = Q/C1 + Q/C2 + Q/C3
    Dividing through by Q, we obtain V/Q = 1/C1 + 1/C2 + 1/C3
    Since V/Q = 1/C
    1/C = 1/C1 + 1/C2 + 1/C3
    Where C is the combined capacitance.
  • In a special case of two capacitors in series, the effective/combined capacitance ,
    C = C1C2/(C 1 + C 2 ).

Capacitors in Parallel

  • When capacitors are arranged in parallel, the potential drop across each of them is the same.
    parallel arrangement of capacitors
    Q1 = C1V, Q2 = C2V, Q3 = C3V
  • The total charge, Q = Q1 + Q2 + Q3
    Q = C1V + C2V + C3V = V(C1 + C2 + C3 )
    Dividing through by V, we obtain Q/V = C1 + C2 + C3
    Since C = Q/V,
    C = C1 + C2 + C3
  • Hence the combined capacitance for capacitors in parallel is the sum of their capacitance.

Example 4.2

  1. In the circuit below, calculate:
    1. The effective capacitance of the capacitors
    2. The charge on each capacitor
    3. The p.d across the plates of each capacitor
      example 4.2
      a. C = (12× 24)/(12 + 24) =8μF
      b. Q1 = Q2 = CV = 8 × 6 = 48μC
      c. V 1 = 48/12 = 4V, V2 = 48/24 = 2V
  2. The figure below shows an arrangement of capacitors connected to a 2V d.c supply.
    1. The combined capacitance of the arrangement
    2. The total charge in the circuit
      ( ans 0.7778μF,3.778μC)
      a. CBD =(3×3)/(3+3) = 1.5μF
      CAE = 2 + 1.5 = 3.5μF
      C = (3.5×1)/(3.5+1) = 0.7778μF
      b. Q = CV = 0.7778 × 2 = 3.778μC.

Assignment 4.1

  • The figure below shows part of a circuit connecting 3 capacitors. Determine the effective capacitance across AC.

Energy Stored by a Capacitor

  • During charging, the addition of electrons to the negatively charged plate involves doing work against the repulsive force.
  • Also the removal of electrons from the positively charged plate involves doing some work against the attractive force.
  • This work done is stored in the capacitor in the form of electrical potential energy.
  • This energy may be converted to heat, light or other forms.
  • A graph of p.d, V against charge, Q is a straight line through the origin whose gradient gives the capacitance of the capacitor.
    energy stored by a capcitor graph
  • The area under this graph is equal to the work done or energy stored in the capacitor.
    i.e. E = ½QV but Q = CV
    Hence E = ½CV2 =Q2/2C

Example 4.3

  1. The figure below shows two capacitors connected to a 12V supply
    example 4.3
    1. The effective capacitance of the circuit
    2. Charge on each capacitor
    3. Energy stored in the combination
      (ans. 18μF, 72μC, 5.46 × 10-3 J)
      a.12+6 = 18μF 
      b. Q1= 12 × 12 = 144μC
      c. E= ½ CV2 = ½ × 18×10-6 × 122 = 5.46 × 10-3 J
  2. In the figure below, calculate the energy stored in the combined capacitor.
    example 4.3 ii
    {ans. 5.4×10-6 )
    C = 2×3 /2+3 =1.2μF
    E = ½ ×1.2 ×10-6 ×22 = 5.4 × 10-6 J

Application of Capacitors

  1. Rectification (smoothing circuits)
    • In the conversion of alternating current to direct current using diodes, a capacitor is used to maintain a high d.c. voltage.
    • This is called smoothing or rectification.
  2.  Reduction of sparking in the induction coil
    • A capacitor is included in the primary circuit of the induction coil to reduce sparking.
  3. In tuning circuits
    • A variable capacitor is connected in parallel to an inductor in the tuning circuit of a radio receiver.
    • When the capacitance of the variable capacitor is varied, the electrical oscillations between the capacitor and the inductor changes.
    • If the frequency of oscillations is equal to the frequency of the radio signal at the aerial of the radio, that signal is received.
  4. In delay circuits
    • Capacitors are used in delay circuits designed to give intermittent flow of current in car indicators.
  5. In camera flash
    • A capacitor in the flash circuit of a camera is charged by the cell in the circuit. When in use, the capacitor discharges instantly to flash.
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