In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has…

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $\mathrm{M}^{\mathrm{P}} \mathrm{L}^{\mathrm{Q}} \mathrm{T}^{\mathrm{R}} \mathrm{A}^{\mathrm{S}}$, where value of ' Q ' and ' R ' are
  1. $(3,-5)$
  2. $(-2,2)$
  3. $(-2,1)$
  4. $(1,-1)$

Solution

$\begin{aligned} & \frac{\phi_{\mathrm{E}}}{\phi_{\mathrm{M}}}=\frac{\mathrm{EA}}{\mathrm{BA}}=\frac{E}{B} \\ & \mathrm{~B}=\frac{\mathrm{M} \ell \mathrm{T}^{-2}}{\mathrm{ATLT}^{-1}} \\ & \text { So }\left[\frac{\mathrm{E}}{\mathrm{B}}\right]=\frac{\mathrm{ML}^{-3} \mathrm{~A}^{-1}}{\mathrm{MT}^{-2} \mathrm{~A}^{-1}}=\mathrm{LT}^{-1}\end{aligned}$
$\begin{aligned} & \text { Or } \\ & E=c \cdot B \\ & {\left[\frac{E}{B}\right]=L T^{-1}}\end{aligned}$

Asked in: JEE Main 2025 (04 Apr Shift 1)

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