Units & Dimensions

JEE Main level, single correct, medium

35 of 149

Question 35 of 149

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of MPLQTRAS\mathrm{M}^{\mathrm{P}} \mathrm{L}^{\mathrm{Q}} \mathrm{T}^{\mathrm{R}} \mathrm{A}^{\mathrm{S}}, where value of ' Q ' and ' R ' are

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Answer: (D) (1,−1)(1,-1)

ϕEϕM=EABA=EB B=MℓT−2ATLT−1 So [EB]=ML−3 A−1MT−2 A−1=LT−1\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}
 Or E=c⋅B[EB]=LT−1\begin{aligned} & \text { Or } \\ & E=c \cdot B \\ & {\left[\frac{E}{B}\right]=L T^{-1}}\end{aligned}

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