Q 12-04-247JEE MainJEE Main 2025 (4 Apr, Shift 1)Medium
In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $M^PL^QT^RA^S$, where the values of $Q$ and $R$ are:
Answer: (D) $(1,\ -1)$
$\dfrac{\phi_E}{\phi_B} = \dfrac{EA}{BA} = \dfrac EB$.
From the Lorentz force, $qE$ and $qvB$ are both forces, so $\dfrac EB$ has the dimensions of a speed (for an EM wave, $E = cB$):
$$\left[\frac EB\right] = LT^{-1} = M^0L^1T^{-1}A^0$$
So $Q = 1$ and $R = -1$.
Solution by Sreeraj P, M.Sc Physics