Let [varepsilon_0] be the dimensional formula | vedclass

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(B) According to Coulomb's law,the force $F$ between two charges $q_1$ and $q_2$ separated by a distance $r$ is given by: $F = \frac{1}{4\pi \varepsil

Vedclass · Accepted Answer

$[\varepsilon_0] = [M^{-1} L^{-3} T^4 A^2]$

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(B) According to Coulomb's law,the force $F$ between two charges $q_1$ and $q_2$ separated by a distance $r$ is given by: $F = \frac{1}{4\pi \varepsilon_0} \frac{q_1 q_2}{r^2}$Rearranging for $\varepsilon_0$: $\varepsilon_0 = \frac{q_1 q_2}{4\pi F r^2}$Substituting the dimensions: $[q] = [AT]$,$[F] = [MLT^{-2}]$,$[r] = [L]$$[\varepsilon_0] = \frac{[AT][AT]}{[MLT^{-2}][L^2]} = \frac{[A^2 T^2]}{[ML^3 T^{-2}]}$$[\varepsilon_0] = [M^{-1} L^{-3} T^4 A^2]$

List-$I$	List-$II$
$(A)$ Angular momentum	$(I)$ $[ML^2T^{-1}]$
$(B)$ Torque	$(II)$ $[ML^2T^{-2}]$
$(C)$ Stress	$(III)$ $[ML^{-1}T^{-2}]$
$(D)$ Pressure gradient	$(IV)$ $[ML^{-2}T^{-2}]$

Let $[\varepsilon_0]$ be the dimensional formula of the permittivity of free space. If $M = \text{mass}$,$L = \text{length}$,$T = \text{time}$,and $A = \text{electric current}$,then which of the following is correct?

Similar Questions

Two quantities $A$ and $B$ are related by the equation $A/B = m$,where $m$ is linear density and $A$ is force. The dimensions of $B$ are equivalent to which of the following?

Match List-$I$ with List-$II$.

List-$I$ List-$II$

$(A)$ Angular momentum $(I)$ $[ML^2T^{-1}]$

$(B)$ Torque $(II)$ $[ML^2T^{-2}]$

$(C)$ Stress $(III)$ $[ML^{-1}T^{-2}]$

$(D)$ Pressure gradient $(IV)$ $[ML^{-2}T^{-2}]$

Choose the correct answer from the options given below:

Of the following,the pair of physical quantities not having the same dimensional formula is

The dimensional formula $M{L^2}{T^{ - 3}}$ represents:

The dimensions of permittivity ${\varepsilon _0}$ are

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