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

We know that the magnetic field \( B \) is related to the permeability \( \mu_0 \) by the equation: \[ B = \mu_0 ni \] The dimensions of \( B \) and \( \mu_0 \) are: \[ [B] = [ni] = [L^{-1} A] \] Thus: \[ \left[ \frac{B}{\mu_0} \right] = L^{-1} A \] Thus, the answer is \( \boxed{\text{L}^{-1} A} \).