Electric and Magnetic fields

CSIR NET and GATE physics

We will now discuss electric and magnetic field vectors (E and B)at a point in the absence of charge.

Now let us place a charge q at point (x,y,z) in space. If this charge experiences a force as given by Lorentz force equation then we can associate vectors E and B with this point (x,y,z) in space.

Thus at any time t vectors E(x,y,z,t) and B(x,y,z,t) gives forces experienced by any charge q at point (x,y,z) with a condition that placing this charge at point (x,y,z) in space does not disturb the position or motion of all other charges responsible for the generation of the field.

So, every point in space is associated with vector E and B which are functions of x,y,z and t.

Since E(or B) can be specified at every point in space , we call it a field.

A field is that physicsl quantity which takes on different values at different points in space for example velocity field of a flowing liquid.

Electromagnetic fields as we know are produced by complex formulas but the relationships between values of the fields at one point and the values of the feld at neighbour points are vary simple and can form differential equations which can completely describe the field.

To understand and visualize the behaviour of field we can consider the field as a function of position and
time. We can also create a mental picture of field by drawing the vectors at many points in space each of which gives strength and direction of field at that point.

Flux is one property of field and flux of a vector field through a surface is defined as the average value of normal component of the vector times the area of the surface.

Another property is the circulation of the vector field and for any vector field circulation around any imagined closed curve is defined as the average tangential component of the vector multiplied by the circumfrance of the loop.

With just the idea of flux and circulation we can define all the laws of electricity and magnetism.
Refrence:- The Feynman lectures on physics Vol 2