Let [{varepsilon _0}] denote the dimensional | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) From Coulomb's law,the force between two charges is given by $F = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{q_1}{q_2}}}{{{R^2}}}$.Rearranging for p

Vedclass · Accepted Answer

$[ {\varepsilon _0} ]=[M^{-1}L^{-3}T^4A^2]$

Vedclass · Answer

(B) From Coulomb's law,the force between two charges is given by $F = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{q_1}{q_2}}}{{{R^2}}}$.Rearranging for permittivity,we get ${\varepsilon _0} = \frac{{{q_1}{q_2}}}{{4\pi F{R^2}}}$.The dimensional formula for charge $q$ is $[AT]$,for force $F$ is $[MLT^{-2}]$,and for distance $R$ is $[L]$.Substituting these into the formula: $[{\varepsilon _0}] = \frac{{[AT][AT]}}{{[MLT^{-2}][L^2]}} = \frac{{[A^2T^2]}}{{[ML^3T^{-2}]}}$.Simplifying the expression,we get $[{\varepsilon _0}] = [M^{-1}L^{-3}T^4A^2]$.

Let $[{\varepsilon _0}]$ denote the dimensional formula of the permittivity of vacuum. If $M =$ mass,$L =$ length,$T =$ time and $A =$ electric current,then:

Similar Questions

The dimensions of pressure are

Give the dimensional formula of the coefficient of viscosity.

Which of the following is dimensionless?

The dimensional formula for volume elasticity is:

The wave equation is given by $Y = A \sin \omega \left( \frac{x}{v} - k \right)$,where $\omega$ is the angular velocity and $v$ is the linear velocity. What is the dimension of $k$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module