Repository of EM Theory Notes and Questions

After a short introduction to units in electricity and magnetism, the electric and magnetic fields are defined in terms of are force experienced by a unit positive charge.

Thomson passed electrons through a region having mutually perpendicular electric and magnetic field, and both perpendicular to the velocity of the electrons. The fields were adjusted so as to produce no deflection. This enabled him to measure the \(e/m\) of electrons. 

The charged particles traveling  perpendicular to electric field, experience a constant force and move along a parabola In this experiment J. J. Thomson discovered that cathode rays consist of charged particles, the electrons, by  demonstrating that the properties of   cathode rays did not depend on the gas in the cathode ray tube.  He measured \(e/m\) of the electrons by analyzing the deflection of cathode rays in electric field. The computational details are presented here. The same principle is used in many devices, a common example being that of an inkjet
printer.

A charged  particle entering a region of uniform magnetic field \(B\) perpendicular to the velocity \(v\) of the charged particle moves in a circle. This motion is called cyclotron motion. The radius and frequency of the circular motion are\(R=\left(\frac{mv}{qB}\right)\qquad \qquad  \omega =\left(\frac{qB}{2\pi m}\right)\),

If a small test charge q is placed at a point and if the force on the charge is \(\bar{F}\) , then the electric field \(\bar{E}\) is defined to be  \[\bar{E}=\bar{F} / q\] where q is positive. unit of \(\bar{E}\) = [\(\bar{E}\)]={Newton/Coulomb}
The test charge must be very small so that it doesn't modify the electric field too much. The magnetic force on a moving charge depends on the direction of velocity;
1.Force is zero when \(\bar{v}\) is parallel to \(\bar{B}\)
2.Force is maximum when \(\bar{v}\) is perpendicular to \(\bar{B}\)
\[\bar{B}= F_{\perp}/q_0\bar{v}\]
Unit of \(\bar{B} =[\bar{B}]=\frac{{N}}{{Coulomb /(m/ s)}}= {N/(amp/m)}={Weber/m^2}\)
\(1 \ {Tesla} = {Weber/{m^2}}= {\mathrm {10^4\ Gauss}}\)

The Hall effect described here provided an early method to study the effect of magnetic field on a current. An expression for Hall voltage and Hall resistance is obtained in this section.