Question

Dimensional formula of e(charge)square upon 4pie epsilon not

Answer 1

Answer: Dimension of q²/4л∈₀ :-

⇒[AT][AT]/[M⁻¹L⁻³T²A²T²]

⇒A²T²/[M⁻¹L⁻³T²A²T²]

⇒[M¹L³T⁻²]

Answer 2

Given:

$Z=\dfrac{e^2}{4\pi\epsilon_o}$

To Find :

The dimensional formula of Z .

Solution :

We know , force is given by :

$F=\dfrac{q^2}{4\pi\epsilon_or^2}$

Therefore ,

$\dfrac{q^2}{4\pi\epsilon_o}=Fr^2\\\\Z=Fr^2$

We know , dimensional formula of Force ( F ) and $r^2$ is given by :

$F=[M\ L\ T^{-2}]\\r^2=[L^2]$

Therefore , dimensional formula of Z is :

$Z=[M\ L\ T^{-2}][L^2]\\\\Z=[M\ L^3\ T^{-2}]$

Learn More :

Units and dimensions

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