Derive the expression between magnteic flux density and magnetic intensity

Magnetic flux density **B **is defined by the force **F** that acts on a charge q moving with a velocity **v **as **F **= q**v **x **B, **where **v **x **B **is the cross product of vectors **v** and **B. **The force is in newtons. So, the dimensions of **B **will be newtons(N)/(coulomb(C)-m/s). So the dimensions of magnetic flux density are Ns/Cm. The units of **B **are weber/m^2. Another way to look at it is through the equation curl **E = **-∂**B**/∂t. This gives the dimensions of B as Vs/m^2 since units of E are volt(V)/m. E is also defined as force per unit charge (from Coulomb’s law of electrostatics). So dimensions of E are N/C. In this way, dimensions of B turn out to be Ns/Cm, the same as before

 

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