Electricity 1

Unlike sound waves, electrical and electromagnetic waves don’t need a medium to propagate through. Before the Michelson- Morley interferometer experiment of 1887, scientists believed that light and other electromagnetic waves travelled through a medium called “ether.” As a result of this failed experiment (it failed to show a medium called ether), scientists recognized that electromagnetic waves can travel through a vacuum. 2

3 Charge is Q = I ¢ t The smallest electrical charge is the elementary charge e, the charge of a single electron. The value of the charge was determined to good accuracy by Millikan in In order to determine the electrical charge, Millikan measured the velocity of charged oil drops in an electrical field. Improved experiments determined with even greater accuracy the value of a charge. The charge has a value of £ Coulombs. Quarks have even smaller elementary charge of e/3.

Electomagnetic waves are agitations of the electromagnetic field. The electical force is always parallel or antiparallel to the electric field. The movement of electrical charges is found in electrical conductors due to the movement of free electrons and in fluids due to the movement of ions. We recognize a difference between conductors, insulators, and semi-conductors. Electrons don’t pile up at the end of a long telephone line because when you phone someone, you are sending along an invisible force field which causes the electrons that are already waiting in your listener’s phone to move. The electrons themself barely travel, instead the force field propagates along the telephone line. 4

5 The electrical field The electrical field can arise due to electrical charges or due to a changing magnet field. The electrical field is a vector field, every point in space is given a vector according to the definition of the electrical field strengths or forces. Electric fields can be represented by field line pictures. Charges are influenced by the electrical field. The following force acts on a charge q F = qE For which E is the electric field vector and q is the charge.

6 Electric field of a positive charge Electric field of two equal but opposite charges (electrical dipole)

7 Electric Field of Two Like Charges

8 Bipolar Field

9 Coulomb’s Law The electric force between two particles with charges of q 1 and q 2 separated by a distance r is given by the equation This is Coulomb’s Law. It is written in terms of a fundamental constant whose value is approximately It is an inverse-square law just like for the gravitational force between two masses. A negative F is interpreted as an attraction between unlike charges and a positive as a repulsion between two like charges. Coulomb's law is actually a special case of Gauss's Law.

10 Problem Consider two small spheres, one carrying a charge of 1 nC (nanocoulomb or Coulomb) and the other a charge of -3 nC, separated by a distance of 4 cm. Find the electric force between them. Solution

11 Gauss’ Law Gauss' Law describes the electrical flux through a closed area. The law uses the concept of flux which is defined for all vector fields. Imagine a body with a charge of Q which is surrounded by an orientated, closed area. Orientated just means that there is an external and internal side. The area can be any form, a sphere or some kind of balloon. The field lines originating from the charge flow through this area. Just like water flows through an area, there is a source and a drain. Because the universe is electrically neutral, all of the field lines that come from a charge must end at another opposite charge. The flux of a charge outside of the area A flows from one side to the other. The total flux thus depends only on the enclosed charge. The main point of the law is that the flux equals charge divided by a nature constant.

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13 Problem Calculate Gauss’ Law for a point charge q placed at the center of a sphere. Solution dA points radially out for a sphere and for reasons of symmetry, E must also be directed radially out and constant in magnet over the surface of a sphere. Thus because E is parallel to dA and cos µ = 1 and because E is constant over the surface A

14 Because the surface area of a sphere is equal to Hence, Gauss’ Law yields or Thus we obtain Coulomb’s Law again.

Lightning Lightning arises as a result of the friction in the clouds. When many small water drops collide in a cloud and create friction, then an electrical current is produced in the cloud. You experience the same sort of friction when your feet rub against the carpeting and cause a charge when you touch the metal door knob (static electricity). At some point the voltage between the clouds is so high that the air becomes a conductor and the charges flow to the earth. A bolt of lightning occurs when the electrons jump from a negatively charged area to a positively charged area. 15

Battery 16 Flow of Anions

17 The Battery A battery consists of portable chemical energie that is transformed to electrical energy as soon as it is put in circuit and discharges itself. Most batteries work with a metal which serves as the minus pole and a metall oxide that serves as the positive pole. The minus pole is also called anode and the plus pole is called cathode. An electrically conducting fluid called the electrolyte bridges the two poles. In order to avoid a short circuit, the anode and cathode are divided by a separator made of plastic or paper. As soon as the battery is placed in a circuit and the poles are brought into contact the process of electrolysis takes place.

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