If $B$ is magnetic field and $\mu_0$ is permeability of free space, then the dimensions of $\left(B /…

If $B$ is magnetic field and $\mu_0$ is permeability of free space, then the dimensions of $\left(B / \mu_0\right)$ is
  1. $\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~A}^{-1}$
  2. $\mathrm{MT}^{-2} \mathrm{~A}^{-1}$
  3. $\mathrm{L}^{-1} \mathrm{~A}$
  4. $\mathrm{LT}^{-2} \mathrm{~A}^{-1}$

Solution

For a current carrying loop at centre
$\begin{aligned}
& B=\frac{\mu_0 i}{2 R} \\ & \therefore \quad \frac{B}{\mu_0} \equiv \frac{i}{R} \equiv\left[\mathrm{AL}^{-1}\right]
\end{aligned}$

Asked in: JEE Main 2025 (22 Jan Shift 1)

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