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જો $\varepsilon_0$ મુક્ત અવકાશની પરાવૈધતાંક અને $\mathrm{E}$ વિધુત ક્ષેત્ર હોય તો $\varepsilon_0 \mathrm{E}^2$ નું પરિમાણ. . . . . . . . .છે.
A$\left[\mathrm{M}^0 \mathrm{~L}^{-2} \mathrm{TA}\right]$
B$\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$
C$\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^4 \mathrm{~A}^2\right]$
D$\left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-2}\right]$
(JEE MAIN-2024)
Solution
$\mathrm{E}=\frac{\mathrm{K}}{\mathrm{R}^2}$
$\mathrm{E}=\frac{\mathrm{Q}}{4 \pi \varepsilon_0 \mathrm{R}^2}$
$\varepsilon_0=\frac{\mathrm{Q}}{4 \pi \mathrm{R}^2 \mathrm{E}}$
$\text { Now, } \varepsilon_0 \mathrm{E}^2=\frac{\mathrm{Q}}{4 \pi \mathrm{R}^2\mathrm{E}} \cdot \mathrm{E}^2=\frac{\mathrm{Q}}{4 \pi \mathrm{R}^2} \cdot \mathrm{E}$
${\left[\varepsilon_0 \mathrm{E}^2\right]=\left[\frac{\mathrm{QE}}{\mathrm{R}^2}\right]=\frac{[\mathrm{Q}][\mathrm{E}]}{\left[\mathrm{R}^2\right]}=\frac{[\mathrm{Q}]}{\left[\mathrm{R}{ }^2\right][\mathrm{Q}][\mathrm{R}]}}$
$=\frac{[\mathrm{W}]}{\left[\mathrm{R}^3\right]}=\frac{\mathrm{ML}^2 \mathrm{~T}^{-2}}{\mathrm{~L}^3}=\mathrm{ML}^{-1} \mathrm{~T}^{-2}$
$\mathrm{E}=\frac{\mathrm{Q}}{4 \pi \varepsilon_0 \mathrm{R}^2}$
$\varepsilon_0=\frac{\mathrm{Q}}{4 \pi \mathrm{R}^2 \mathrm{E}}$
$\text { Now, } \varepsilon_0 \mathrm{E}^2=\frac{\mathrm{Q}}{4 \pi \mathrm{R}^2\mathrm{E}} \cdot \mathrm{E}^2=\frac{\mathrm{Q}}{4 \pi \mathrm{R}^2} \cdot \mathrm{E}$
${\left[\varepsilon_0 \mathrm{E}^2\right]=\left[\frac{\mathrm{QE}}{\mathrm{R}^2}\right]=\frac{[\mathrm{Q}][\mathrm{E}]}{\left[\mathrm{R}^2\right]}=\frac{[\mathrm{Q}]}{\left[\mathrm{R}{ }^2\right][\mathrm{Q}][\mathrm{R}]}}$
$=\frac{[\mathrm{W}]}{\left[\mathrm{R}^3\right]}=\frac{\mathrm{ML}^2 \mathrm{~T}^{-2}}{\mathrm{~L}^3}=\mathrm{ML}^{-1} \mathrm{~T}^{-2}$
Standard 11
Physics
Similar Questions
લીસ્ટ $I$ સાથે લીસ્ટ $II$ યોગ્ય રીતે જોડો.
| લીસ્ટ $I$ (ભૌતિક રાશી) | લીસ્ટ $II$ (પારિમાણિક સૂત્ર) |
| $(A)$ દબાણ પ્રચલન | $(I)$ $\left[ M ^0 L ^2 T ^{-2}\right]$ |
| $(B)$ ઊર્જા-ઘનતા | $(II)$ $\left[ M ^1 L ^{-1} T ^{-2}\right]$ |
| $(C)$ વિદ્યુતક્ષેત્ર | $(III)$ $\left[ M ^1 L ^{-2} T ^{-2}\right]$ |
| $(D)$ ગુપ્ત ઉષ્મા | $(IV)$ $\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]$ |
