Oscillating Electromagnetic Field

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When a moving charged particle enters a magnetic field perpendicularly, it is acted upon by a force whose direction is given by Fleming's left-hand rule. Because of this force, the particle deflects from its original path and moves along a circular path.

Suppose a charged particle, as an electron (charge - e), moving with velocity v* enters perpendicularly a uniform magentic field B (Fig. 4). The magnetic field B is perpendicular to the plane of the paper, directed downwards. The magnitude of the force F acting on the electron due to the field B* is given by F = evB . The force F* is perpendicular to the velocity v in the plane of the paper and is directed downwards. Since this force is perpendicular to velocity, the magnitude of the velocity (speed) of the electron does not change, but its direction changes continuously. Hence, the electron moves on a circular path in clockwise direction with uniform speed v. Thus, the velocity and the force are always perpendicular to each other. The force F acts as the necessary centripetal force for the electron.

If m be the mass of the electron and r the radius of its path, ...
... then the magnitude of the centripetal force will be mv/r. Hence

2

r-r „ m V F = evB = -

or m v is the momentum of the electron. Thus, the trajectory of an electron in a magnetic field is circular and the radius of the path is proportional to the momentum of the elecirun.

When the electron leaves the magnetic field, the magnetic force vanishes and the electron moves in a straight line.

We have read in chapter 1 that the trajectory of an electron entering perpendicularly a uniform eleetric field is parabolic.

Difference in behaviour of Charged Particle in Electric and Magnetic Fields

The followings are the differences in the behaviour of a charged particle in electric and magnetic fields :

(i) A charged particle, whether stationary or moving, always experiences a force in an electric field. But, in a magnetic field, a charged particle experiences a force only when it is in motion and the direction of motion is not parallel or antiparallel to the direction of the magnetic field.

(ii) The direction of electric force on a charged particle is in the direction of the electric field (if particle is positively charged) or opposite (if particle is negatively charged); while the direction of magnetic force is perpendicular to the magnetic field.

(iii) The kinetic energy of the charged particle moving in electric field changes, while it does not change in magnetic field.

(iy) The trajectory of the charged particle entering an electric field perpendicularly is parabolic, while the trajectory of the charged particle entering a magnetic field perpendicularly is circular.

Electromagnetic waves
Light and other electromagnetic waves
Light is not the only example of an electromagnetic wave. Other electromagnetic waves include the microwaves you use to heat up leftovers for dinner, and the radio waves that are broadcast from radio stations. An electromagnetic wave can be created by accelerating charges; moving charges back and forth will produce oscillating electric and magnetic fields, and these travel at the speed of light. It would really be more accurate to call the speed "the speed of an electromagnetic wave", because light is just one example of an electromagnetic wave.

speed of light in vacuum: c = 3.00 x 108 m/s

As we'll go into later in the course when we get to relativity, c is the ultimate speed limit in the universe. Nothing can travel faster than light in a vacuum.

Check this Momentum Equation Physics awesome i recently used to see.

There is a wonderful connection between c, the speed of light in a vacuum, and the constants that appeared in the electricity and magnetism equations, the permittivity of free space and the permeability of free space. James Clerk Maxwell, who showed that all of electricity and magnetism could be boiled down to four basic equations, also worked out that:

This clearly shows the link between optics, electricity, and magnetism.
Creating an electromagnetic wave

We've already learned how moving charges (currents) produce magnetic fields. A constant current produces a constant magnetic field, while a changing current produces a changing field. We can go the other way, and use a magnetic field to produce a current, as long as the magnetic field is changing. This is what induced emf is all about. A steadily-changing magnetic field can induce a constant voltage, while an oscillating magnetic field can induce an oscillating voltage.

Focus on these two facts:

1. an oscillating electric field generates an oscillating magnetic field
2. an oscillating magnetic field generates an oscillating electric field

Those two points are key to understanding electromagnetic waves.

An electromagnetic wave (such as a radio wave) propagates outwards from the source (an antenna, perhaps) at the speed of light. What this means in practice is that the source has created oscillating electric and magnetic fields, perpendicular to each other, that travel away from the source. The E and B fields, along with being perpendicular to each other, are perpendicular to the direction the wave travels, meaning that an electromagnetic wave is a transverse wave. The energy of the wave is stored in the electric and magnetic fields.
Properties of electromagnetic waves

Something interesting about light, and electromagnetic waves in general, is that no medium is required for the wave to travel through. Other waves, such as sound waves, can not travel through a vacuum. An electromagnetic wave is perfectly happy to do that.

An electromagnetic wave, although it carries no mass, does carry energy. It also has momentum, and can exert pressure (known as radiation pressure). The reason tails of comets point away from the Sun is the radiation pressure exerted on the tail by the light (and other forms of radiation) from the Sun.

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