Electricity and Magnetism

Current Electricity

Electric current is the rate of flow of electric charge through a conducting medium with respect to time. It is caused by drift of free electrons through a conductor to a particular direction.Charges in motion constitute an electric current. Such currents occur naturally in many situations. Lightning is one such phenomenon in which charges flow from the clouds to the earth through the atmosphere, sometimes with disastrous results. The flow of charges in lightning is not steady, but in our everyday life we see many devices where charges flow in a steady manner. A torch and a cell-driven clock are examples of such devices. Conventionally, the direction of current is taken as the direction in which a positive charge moves. The electrons move in the opposite direction.

The current is the rate of flow of charge through a surface area placed perpendicular to the direction of flow. If charge ?q flows in time ?t, the average current is defined as :

q I av = ———– t

Ohm’s Law:-

A basic law regarding flow of currents was discovered by G.S. Ohm in 1828. Imagine a conductor through which a current I is flowing and let V be the potential difference between the ends of the conductor. Then Ohm‘s law states that :- V? Ior, V = R I

Resistance and Resistivity :-Resistivity ? is an intrinsic property of a material and directly proportional to the total resistance R, an extrinsic quantity that depends on the length and cross-sectional area of a resistor.

The resistivity of a material is found to be dependent on the temperature. Different materials do not exhibit the same dependence on temperatures. Over a limited range of temperatures, that is not too large, the resistivity of a metallic conductor is approximately given by, ?(T) = ?(0) [1 + ? (T– T(0) )]

Series and Parallel circuits Resistance

A series circuit is a circuit in which resistors are arranged in a chain, so the current has only one path to take. The current is the same through each resistor. The total resistance of the circuit is found by simply adding up the resistance values of the individual resistors:

equivalent resistance of resistors in series : R = R1 + R2 + R3 + …

A parallel circuit is a circuit in which the resistors are arranged with their heads connected together, and their tails connected together. The current in a parallel circuit breaks up, with some flowing along each parallel branch and re-combining when the branches meet again. The voltage across each resistor in parallel is the same.

The total resistance of a set of resistors in parallel is found by adding up the reciprocals of the resistance values, and then taking the reciprocal of the total:

equivalent resistance of resistors in parallel: 1 / R = 1 / R1 + 1 / R2 + 1 / R3 +… Krichoff Rules:-

Kirchhoff’s junction rule states that the algebraic sum of the currents at any branch point or junction in a circuit is zero. Symbolically, we may write , below, as the sum of n currents flowing into a junction:

Kirchhoff’s second rule states that the algebraic sum of the potential changes around any complete loop in the network is zero. Again we may write , symbolically ,as the sum of the potential changes:

Moving Charge and Magnetism

Magnetism is a phenomenon produced by the motion of electric charge, which results in attractive and repulsive forces between objects.

A magnet is any piece of material that has the property of attracting iron (or steel). Magnetite, also known as lodestone, is a naturally occurring rock that is a magnet. This natural magnet was first discovered in a region known as magnesia and was named after the area in which it was discovered. Magnetism may be naturally present in a material or the material may be artificially magnetized by various methods.

Magnets may be permanent or temporary. After being magnetized, a permanent magnet will retain the properties of magnetism indefinitely. A temporary magnet is a magnet made of soft iron, that is usually easy to magnetize; however, temporary magnets lose most of their magnetic properties when the magnetizing cause is discontinued. Permanent magnets are usually more difficult to magnetize, but they remain magnetized. Materials which can be magnetized are called ferromagnetic materials.

The force exerted on a charged particle by a magnetic field is given by the vector cross product: F = q ( v x B ) F = force (vector) q = charge on the particle (scalar) v = velocity of the particle relative to field (vector) B = magnetic field (vector)

Electromagnetic Wave

Electromagnetic Wave are waves composed of undulating electrical fields and magnetic fields. The different kinds of electromagnetic waves, such as light and radio waves, form the electromagnetic spectrum. All electromagnetic waves have the same speed in a vacuum, a speed expressed by the letter c (the speed of light) and equal to about 186,000 miles (or 300,000 kilometers) per second. Electromagnetic Wave transport energy, due to oscillating electric and magnetic fields, Electromagnetic Waves are called electromagnetic radiation, light, or photons.

Maxwell‘s equations predicts the existence of electromagnetic waves that travel with speed of light c =1/ μ ? . The reason is due to the fact that a changing electric field produces a magnetic field and vice versa, and the coupling between the two fields leads to the generation of electromagnetic waves.

The Biot-Savart law asserts that the magnetic field dB due to an element dl carrying a steady current i at a point P at a distance r from the current element is:

Four Maxwell equations are:-

In 1887, Heinrich Hertz generated and detected electromagnetic waves in his lab. The waves radiated from a transmitter circuit and were detected in a receiver circuit. Hertz used the fact that electrical circuits have resonant frequencies just like mechanical systems do.

 A stationary charge produces an electric field.

 A charge moving at constant speed produces electric and magnetic fields.

 A charge that is accelerated will produce variable electric and magnetic fields. These are electromagnetic waves.

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