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

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The SI units in use in electromagnetic theory are explained and values of some important  constants given.

 1.1 Defining the Electric and Magnetic Fields 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 $$\bar{B} =[\bar{B}]=\frac{{N}}{{Coulomb /(m/ s)}}= {N/(amp/m)}={Weber/m^2}$$$$1 \ {Tesla} = {Weber/{m^2}}= {\mathrm {10^4\ Gauss}}$$ 1.2 Units and Dimensions in E. M. Theory 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.

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