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### Introduction to Electricity and Magnetism!!!!

There is a study of electricity and magnetism which involves the interaction of large number of charged particles with each other through their electric field and magnetic fields. The word “Charged particles” in here means particles that are electrically charged, that means those particles which can exert forces on each other and those which obey the equations governing electric and magnetic interactions. For two objects, both are less than the size of mountains, the electric force between the objects; if non-zero, is generally much larger than the gravitational force between the objects.

The gravitational force between two ordinary objects is usually too small to be detectable, while the electric and magnetic forces between the two objects can be devastatingly strong, as in lightning and in other electrical discharges.

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The Electric Field.

There is a value for the electric field E which is not zero (  non-zero value) at a point in space at a particular time if a charged particle, being at that point at that time, would feel a force that is linearly proportional to the particle’s charge in this way:

F  = qE

The Magnetic Field:

There is an another field in which there is a non-zero value that means those values which have magnitude apart from zero at a point in space at a particular time if a charged particle, being at that particular point at that particular time, would feel a force that is linearly proportional to the particle’s charge and velocity in given way as follows:

F  = q v × B

Here q is the electric charge on that particle.

Here is the interesting fact to note that the force is at right angles or perpendicular to both the velocity vector v and the magnetic field vector, and that the magnetic field force is zero if the velocity is along the direction of the magnetic field B. Thus to determine for the presence of a magnetic field B one must try several orientations for the charged particle’s velocity.

The Equations Summarized.

Here is the Maxwell’s Equations which implies:

• The electric charges produce electric fields;
• There is no magnetic charge to produce magnetic fields, no magnetic analog to electric charge;
• The time-changing magnetic fields produce electric fields; and
• Electric currents and time-changing electric fields produce magnetic fields. The Lorentz Force on a particle with charge q and velocity ~v, moving in both an electric field E and a magnetic field B, is:

F  = qE + qv × B .

The Vector Product of A  and B  , is itself a vector and we will show separately how to find its magnitude and direction.

The vector product is called the “cross product” because of the way it is represented visually:

C  = A  × B  .

Also,

|C  | = |A  × B  | = AB sin θ.

The direction of the vector C is perpendicular to the plane which is formed by A and B  and that narrows it to one of two directions.