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Chapter 4

The Concept of a Field

4.1Action at a distance

According to Newton’s Third Law, when an object A exerts a force on an object B, object B simultaneously exerts an equal and opposite force on object A (Ch. 2). My weight exerts a downward force on the floor, and the floor exerts an equal upward force on my body. This upward force, called a normal force, is an example of a contact force. When I hit a ball with a tennis racket, the force applied by the ball to the racket and that applied by the racket to the ball are examples of contact forces. But the force of gravity is a different kind of force. There is no contact between the apple and the earth, and yet there is a force. There is no contact between the earth and the sun, but the force of gravity keeps the earth revolving round the sun. Gravity is an example of a non-contact force, also called action at a distance.

Our eyes enable us to see the sun in the sky. But how does the earth know the sun is out there, 150 million kilometers away? It feels the force of gravity. Newton did not probe into the precise mechanism by which the sun communicates its influence upon the earth. He was interested only in the effects of gravity, not how the force of gravity is communicated between objects. But this question did come up, and physicists answered it by creating the concept of a field. The word field means a region of influence between the objects that experience a mutual force. Our current understanding of the gravitational field is due to the General Theory of Relativity published by Einstein in 1915. A gravitational mass such as the sun has an influence on the space that surrounds it. This influence is communicated in all directions through the space. This influence is called the gravitational field of the sun. Any object that enters this gravitational field experiences an attraction towards the sun. The strength of the gravitational field decreases with distance. So the sun’s gravitational field experienced by Mercury is much greater than that experienced by Neptune. Each planet also generates its own gravitational field. The moon is subjected to the gravitational field of the earth and is attracted to the earth. Of course, the moon also has its own gravitational field which is weaker than that of the earth because the moon is so much smaller than the earth. The actual gravitational field between the earth and the moon has a contribution from both the earth and the moon. And this is true for all pairs of objects in the universe.

So the gravitational field mediates the forces between objects. The moon cannot really “see” the earth. It “feels” the gravitational field, and this field “tells” the moon that there is an object of such a mass at such a distance away. Likewise the earth feels the gravitational field between itself and the sun, and responds accordingly.

Thus, the concept of a gravitational field eliminates the need for action at a distance. All action is contact action. An apple accelerates towards the ground because it interacts with the gravitational field between itself and the earth. It does not actually “know” there is an earth out there until it hits the ground, at which point there is a contact force between the apple and the ground.

4.2Electricity and magnetism

Gravity was the only long range force known to humans for a long time until the discovery of magnetism and electricity. When magnetism was discovered, people were puzzled by the phenomenon. A magnetized bar of iron seemed no different from before it was magnetized — in mass, shape, color, temperature, etc. A suspended magnet aligned itself in the northsouth direction. So it appeared that the magnet had tapped into some unknown power from space. Today we call it the earth’s magnetic field. Every magnet has two poles, a north seeking pole and a south seeking pole, and it is impossible to isolate a magnetic pole. If we were to divide a magnet in half, we would get two smaller magnets, each with a north and a south pole. The difference between the magnetic and the gravitational fields is that whereas the gravitational field always produces attraction between two objects, a magnetic field produces repulsion between two like poles and attraction between unlike poles. Similar to the gravitational field, the magnetic field due to a magnetic pole becomes weaker with the distance from the pole.

A magnetic field is often represented in books by lines called magnetic lines of flux. Lines can be imagined as flowing out of a north seeking pole and ending in a south seeking pole. The direction of the force experienced by a magnetic pole at any point in a magnetic field is given by the direction of the flux line at that point. A north pole would tend to move in one direction along the line, and a south pole would tend to move in the opposite direction.

The source of magnetism had to remain a mystery until the discovery of electricity. It was surely one of the most thrilling moments in the history of science when they found that a magnet was affected by the flow of electric current in a nearby wire.

Electric current is the flow of electric charges. And like magnetic poles, electric charges come in two opposite varieties, which we call positive and negative. Similar to magnets, unlike charges attract and like charges repel. But in contrast to magnets, it is possible to isolate charges. Every charge generates its own electric field. So a positive charge will sense the presence of another charge in the vicinity by picking up the electric field produced by the other charge. This field will tell the positive charge if the other charge is positive or negative. The strength of the field diminishes with distance, just like magnetic and gravitational fields.