Question

If \( B \) is magnetic field and \( \mu_0 \) is permeability of free space, then the dimensions of \( \frac{B}{\mu_0} \) is:

• A. \( \text{MT}^{-2} A^{-1} \)
• B. \( \text{L}^{-1} A \)
• C. \( \text{LT}^{-2} A^{-1} \)
• D. \( \text{ML}^2 T^{-2} A^{-1} \)

Hint:

The dimension of \( B/\mu_0 \) can be derived from the relationship of magnetic field with current and charge density.

Answer 1

The Correct Option is B

To determine the dimensions of the expression \( \frac{B}{\mu_0} \), where \( B \) represents the magnetic field and \( \mu_0 \) is the permeability of free space, we start with their respective dimensional formulas.

The magnetic field \( B \) has the dimensions \([B] = \text{MT}^{-2}A^{-1}\).

The permeability of free space \( \mu_0 \) has the dimensions \([\mu_0] = \text{MLT}^{-2}A^{-2}\).

Calculating the ratio \(\frac{B}{\mu_0}\):

\(\frac{B}{\mu_0} = \frac{\text{MT}^{-2}A^{-1}}{\text{MLT}^{-2}A^{-2}}\)

Simplifying this expression yields:

\(\frac{B}{\mu_0} = \frac{\text{M}^{1-1}\text{T}^{-2+2}\text{A}^{-1+2}}{\text{L}^{1}}\)

The resulting dimensions are \(\text{L}^{-1}\text{A}^{1}\).

Consequently, the dimensions of \(\frac{B}{\mu_0}\) are \(\text{L}^{-1}A\).