Find the dimensions of
A. electric field E,
B. magnetic field B and
C. magnetic permeability μ0.
The relevant equations are
and
where F is force, q is charge υ is speed, I is current, and a is distance.
A. Electric field is defined as the electrical force per unit electrical
charge.
Dimensions of F = [MLT-2]
Dimensions of q = [AT]
Dimensions of E = .
B. Magnetic field is defined as the space around which the effect of a magnetic force can be felt. For a charge q, moving with velocity v in a magnetic field of strength B, the magnetic force F is given by
For simplicity let us take to be simply qvB.
So, B will become
Dimensions of F = [MLT-2]
Dimensions of q = [AT]
Dimensions of v = [LT-1]
Dimensions of B = .
C. Magnetic permeability is defined as the amount of magnetization a body can acquire. For a wire carrying current I, the magnetic field B produced at a radial distance a is given by the relation
Here μ0 is the magnetic permeability of free space.
From the above relation we can write
Dimensions of a = [L]
Dimensions of B =
Dimensions of I = [A]
Dimensions of μ0 = = [MLT-2A-2]