[NOTES/EM-01001] Units and Dimensions in E. M. Theory

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 \(\bar{B} =[\bar{B}]=\frac{{N}}{{Coulomb /(m/ s)}}= {N/(amp/m)}={Weber/m^2}\)
\(1 \ {Tesla} = {Weber/{m^2}}= {\mathrm {10^4\ Gauss}}\)

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.