ELECTROSTATICS II.

Specific objectives.

• Define capacitance.
• Sketch electric field patterns around a charged body.
• Describe charge distribution on conductors of various shapes.
• Explain lightning arrestors.
• Define capacitors and state its SI unit.
• Describe charging and discharging a capacitor.
• State the factors affecting the capacitance of a parallel place capacitor.
• Solve numerical problems involving capacitors.
• State the application of capacitors.

                                                Electric field.

• A region or space around a charged body where other charged bodies experience a force of attraction or repulsion.
• It is defined by line of force or it is represented by field lines.

                                                Lines of force.

• A path followed by a positive charge in an electric field.
• Starts from the positive charge and ends to the negative charge.

                                                Types of electric field.

Strong field.

• A field where the lines of force are so many and are close together.

Weak field.

• A field where the lines of force are few and are far apart.

Uniform field.

• A field where the lines of force are equally spaced and parallel.

                                                Characteristics of lines of force.

• They do not cross each other or meet.
• They come from a positive charge and converge at a negative charge.
• They leave the body at right angle.

                                                Force on a charged body.

• Two charged bodies will attract or repel each other.
• The force on these bodies depends on

1. The quantity of charge they have.
2. The distance between them

• The force F is directly proportional to the product of the charges.

            F  Q₁Q₂

• The force is inversely proportional to the square of the distance between the charges.

            F

                                                The field patterns.

1. Field around a positive charge.
2. Field around a negative charge.
3. Two unlike charges.
4. Two like charges.
5. Two parallel plates.
6. An isolated positive charge.

Field patterns.

• A neutral point is a region between two like charges where there are no lines of force or where the resultant force is zero.

                                                Distribution of charges on a charged body.

• The distribution of charges on a charged body is determined by the shape of the body.
• A body with uniform surface area, the charges are uniformly distributed.
• A non- uniform body surface area, the charges are highly concentrated at the sharp point.

• To investigate the distribution of charges in the above bodies, a charged electroscope and a proof plane are used. The proof plane is used to collect charges from each body by touching then taking it near the cap of the charged electroscope. The deflection of the leaf is noted for every part of the body.

                                                Results.

• The deflection from the metal sphere is the same for all parts of the body.
• The peer shaped deflection is greater at the sharp point than the rest of the surface. This shows that there is high concentration of charges at the sharp point.

                                    Effect of high concentration of charges at the sharp point.

• These charges create a strong electric field which ionizes the air around. The charges on the body attracts the opposite charges in the air and gets discharged. The remaining charges flow in the air as electric wind.
• A charged body with a sharp point discharges faster than the one of uniform surface.

                                                Charges on a sharp point.

• A sharp point contains extremely a high concentration of charges which create a strong electric field which ionizes the air around it, hence becomes discharged. This is called point charged action.
• The point charged action can be demonstrated by using a thin wire connected to a Vander wall Graff generator.

                                                Observation.

• The flame is diverted as if there was a wind emmenating from the wire. This phenomenon is known as electric wind.

                                                Discussion.

• If the charge on the wire is positive, the high concentration of charges on the wire causes ionization of the surrounding air producing electrons and positive ions. The electrons move towards the wire while the heavy positive ions drift towards the flame forming an electric which direct the flame. If the wire is brought very close to the flame, the flame split into two sections.

                                                Explanation.

• Negative ions in the flame are attracted by the positive charges on the wire directing part of the flame towards it. The positive ions are repelled away diverging part of the flame away. The point charge action is used to discharge aircraft and as lightning arrestor.

                                                            Lightning arrestor.

• It’s a metal conductor with a sharp point at one end metal plate which is buried near a building.
• It is used to prevent building from being destroyed by lightning. It is made of copper.

                                                            How it works.

The arrestor is erected near the building with the sharp point over the structure and the metal plate to the ground. During thunderstorm, the ground and the cloud are oppositely charged. If the cloud is negatively charged, the ground and the arrestor are positively charged. There are high concentration of charges of the spitos of the arrestors which develop a strong field. The strong field ionizes the air around. The point attracts all the negative ions from the air and conducts them to the ground. The positive ions are attracted by the cloud hence discharging it. This lowers electric field between the ground and the cloud to a level that lightning can occur through the building.

                                                Charge on a hollow conductor.

• A charged hollow conductor has charges only on the outside. No charges on the inside.
• Airplanes and vehicles are hollow conductors hence no effect of electrostatic on its inside.

                                                            Capacitor.

• Electrical device used to store electrical energy (electric charges).
• It is made of two conducting plates separated by an insulator. This is called dielectric.

                                                Types of capacitors.

• There are three main types of capacitors.
• They will differ in geometrical shapes and sizes.

1. Fixed area capacitor.

• The area between the plates is fixed.
• The space between the plates contain a dielectric substance which determine the type of capacitor.
• Example;

1. Paper capacitor consists of two long strip of metal foil between which are the strips of paper.
2. Plastic capacitor contain plastic as the dielectric.
3. Ceramic capacitor contain ceramic as dielectric.
4. Mica capacitor contain mica as dielectric.

1. Variable area capacitor.

• The area between the plates can be varied.
• It contains air between the plates as dielectric.
• It consists of fixed metal vanes connected to a metal frame of the capacitor and movable metal vanes joined to the central metal shaft and turned by a control knob.
• Used as tuning the radio and TV.

1. Electrolytic capacitor.

• They contain an electrolyte aluminum borate soaked in a paper and aluminum foil.
• When the current is passed through for some time, a very thin film of aluminum oxide is formed on the anode.
• The film is an insulator and therefore act as the di- electric.

                                                Charging of a capacitor.

• A capacitor is charged by using a direct current.
• The circuit consists of a capacitor, a d.c source of 6V, a high resistance wire, a milliammeter and a voltmeter.

• When the switch S is closed, the milliameter reading increases from zero to maximum then to zero as the capacitor takes a short time. The voltmeter reading increases to maximum after some time. During charging, electrons flow from the negative terminal of the cell to the negative plate of the capacitor. At the same rate, negative charges slow from the other positive plate of the capacitor towards the positive terminal.
• As the charges increase, the p.d across the capacitor or the plates increases and the charging current decreases. When the capacitor is fully charged, the charging current reduces to zero. The p.d across the capacitor is equal to the p.d of the cell. The charge stored will be minimum when the two p.d’s are equal and co current flows.

                                                Discharging a capacitor.

• When a charged capacitor is connected in series with a resistor and a milliammeter, the reading on the milliameter reduces from maximum to minimum value and the deflection in opposite direction. The capacitor is said to have been discharged.

                                                Capacitance.

• The charge stored in a capacitor is directly proportional to the voltage

            Q  V

            Q = KV

            Q = CV

• The charge stored by a capacitor per unit voltage across the field.

            Q = CV

C =                                        SI units = farad (f)

• Capacitance is a measure of amount of charge the capacitor can store when connected to a given voltage.

                                    Factors affecting capacitance.

1. Area of the plates overlapping.
2. Their capacitance is directly proportional to the area of the plates, that is, the area of overlap.
3. A large plate stores more charges hence more capacitance.
4. Distance between the plates.
5. The capacitance is inversely proportional to the distance of separation between the plates.
6. Medium between the fields.

• Capacitance increases when the insulating medium between the plates is solid e.g. paper, glass instead of air.

            C

            C =

                                  whereis dielectric constant when the material is air

                                     SI unit = f/m

                                                Capacitance network.

• Capacitors can be arranged in parallel or series in a circuit.
• In each arrangement, a combined or equivalent capacitance can be calculated.

                        Parallel arrangement.

• Two or more capacitors can be arranged in parallel.
• In this arrangement;

1. The p.d across each capacitor is the same.
2. The charge stored in each capacitor is different.

Example.

Three capacitors of capacitance C₁, C₂ and C₃ are connected in parallel.

      Total charge     Q = Q₁ + Q₂ + Q₃

      But Q_T = C_T V_T

      Q₁ = C₁ V         Q₂ = C₂ V            Q₃ = C₃ V

        Q_T= C_T V_T = C₁V + C₂ V + C₃ V

      C_T V_T = V(C₁ + C₂ + C₃)

      C_T = C₁ + C₂ + C₃

• The total or equivalent capacitance in parallel arrangement is the sum of the capacitance in parallel.

                                    Series arrangement.

• Three capacitors of capacitance 1, 2 and 3 can be arranged in series.
• In this arrangement;

1. The charge stored in each capacitor is the same.
2. The p.d across each capacitor is different.

Total voltage V = V + V 

• The equivalent capacitance in series is less than the smallest capacitance in that arrangement.

                                    Energy stored in a capacitor.

• The capacitor stores electrical energy which can be converted to heat, light or mechanical energy.
• When the capacitor is charged, the p.d across its plate is directly proportional to the charge stored.
• A graph of p.d against the charge is a straight line passing through the origin.

            Q  V

            Q= CV

• The gradient of the graph represent capacitance and the area under the graph is the work done in moving a charge Q through a p.d V.

                                    Uses of capacitors.

1. Reduce sparking in induction coil (contact point) in ignition system of vehicles.