Dimensions of B by Mu Zero Shortcut

 

❓ Question

If $B$ is the magnetic field and $\mu_0$ is the permeability of free space, find the dimensions of

$$\frac{B}{\mu_0}$$

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✍️ Solution

We know the relation

$$B=\mu_0 H$$

where $H$ is the magnetic field intensity.

Therefore,

$$\frac{B}{\mu_0}=H$$

So,

$$\left[\frac{B}{\mu_0}\right]=[H]$$

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Step 1: Dimension of magnetic field intensity

The SI unit of $H$ is

$$\text{A m}^{-1}$$

Therefore,

$$[H]=[AL^{-1}]$$

Hence,

$$\left[\frac{B}{\mu_0}\right] = [AL^{-1}]$$

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✅ Final Answer

$$\boxed{\left[\frac{B}{\mu_0}\right]=[L^{-1}A]}$$

or equivalently,

$$\boxed{[M^0L^{-1}T^0A^1]}$$

Key Idea

Using

$$\boxed{B=\mu_0H}$$

directly gives

$$\boxed{\frac{B}{\mu_0}=H}$$

whose unit is ampere per metre $(\text{A/m})$.