Q 11-01-051JEE MainJEE Main 2026 (8 Apr, Shift 2)Medium
Consider the equation $H = \dfrac{x^p \epsilon^q E^r}{t^s}$
Where $H =$ magnetic field; $E =$ electric field, $\epsilon =$ permittivity, $x =$ distance, $t =$ time. The values of $p, q, r$ and $s$ respectively are :
Answer: (A) $1, 1, 1, 1$
Here $H$ is the magnetising field, with unit A m$^{-1}$.
$\epsilon E$ has the unit of surface charge density: $\epsilon E = \dfrac{\sigma}{1}$ (for example, near a charged plate $E = \sigma/\epsilon$), so $[\epsilon E] = \text{C m}^{-2}$.
Then $\dfrac{x\,\epsilon E}{t}$ has unit $\dfrac{\text{m} \times \text{C m}^{-2}}{\text{s}} = \dfrac{\text{C}}{\text{s}}\cdot\dfrac{1}{\text{m}} = \text{A m}^{-1}$, which is the unit of $H$.
So $p = q = r = s = 1$.
Solution by Sreeraj P, M.Sc Physics