- Charge Distribution on the Surface of a Conductor
- Application of Static Charges
- Dangers of Static Charges
- Electric Field
- 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.
- 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:
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- The electric field pattern between two charged bodies obeys the law of electrostatics.
- Below are some patterns between charged bodies:
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.
Experiment: To Charge a Capacitor
Apparatus : Uncharged capacitor of 500μF, 5.0V power supply, rheostat, voltmeter, milliammeter, switch, connecting wires and a stop watch.
- Set up the apparatus as shown above.
- 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)
- Plot a graph of current, I against time, t
- 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:
- 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.
NB The product It represents the amount of charge in the capacitor.
Experiment: To Discharge a Capacitor
Apparatus : A charged capacitor, resistor, galvanometer, switch and connecting wires.
- Set up the apparatus as shown above.
- 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)
- 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.
- 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.
- 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