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]