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Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Electric Field and Potential

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Electric Field and Potential

Determine the dimensional formula of _0 .

Determine the dimensional formula of

\varepsilon_0

.

Options

A $M^{-1} L^{-3} T^4 I^2$
B $M L^3 T^{-4} I^{-2$
C $M^{-1} L^{-3} T^3 I$
D $M^{-1} L^{-2} T^4 I^2$

Correct answer

A. $M^{-1} L^{-3} T^4 I^2$

Step-by-step solution

Using Coulomb's law:

F = \dfrac{1}{4\pi\varepsilon_0} \dfrac{q_1 q_2}{r^2}

Rearranging for

\varepsilon_0

:

\varepsilon_0 = \dfrac{q_1 q_2}{4\pi F r^2}

Substituting the dimensional formulas for charge

[q] = I T

, force

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

, and distance

[r] = L

:

[\varepsilon_0] = \dfrac{[I T] [I T]}{[M L T^{-2}] [L^2]}

[\varepsilon_0] = \dfrac{I^2 T^2}{M L^3 T^{-2}}

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

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