COIL, THE KING OF ELECTRICITY

We know electron whirls and spins in an atom. When an electron revolves, the electric fields also circulates. Consequently a magnetic field is created perpendicular to the plane of rotation(maxwell's equation).

Suppose in a loop of wire, a current (bunch of electrons) flows, a magnetic field will be created through the loop. One side north pole and the other side south pole. We will extend this principle further. If we have a coil of wire (more number of loops). The magnetic fields are added up and we get a strong magnetic field. In short, the current carrying coil acts like a bar magnet with north pole at one end and the south pole at the other end.

Now we will do a simple experiment to demonstrate magnetism created by a coil. Wire the circuit as given below.

Here, when the switch is closed, the current flows through the coil only. Current cannot pass through LED because it is a one way device. While the current flows through the coil, magnetic field builds up in the coil and reaches the saturation value.

Now open the switch, the battery is cut off. The magnetic field in the coil starts to collapse. The collapsing magnetic field creates opposite voltage, opposite current in the coil (Faraday's law).
Now the current flows through the LED and illuminates it for a brief time. This proves the creation and destruction of magnetism in the coil.

Applications: Microphone coverts voice into varying electric current. This current is amplified and fed into the speaker. The changing current pass through the coil in the speaker. Hence changing magnetic field is created in it. This causes coil to vibrate (Lawrence force). The attached diaphragm also vibrates producing loud sound (A simple explanation).

The coil is the main part in all the motors, meters, transformers, all electronic devices, house hold electrical devices etc. We know "coil winding" is a trade and educational course. So the simple coil of copper wire plays a major role in electrical engineering.

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LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. Inverted parabola shape is used in the construction of buildings and bridges. Because the shape is able to bear more weight. A plane

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

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