Units & Dimensions

JEE Main level, single correct, medium

27 of 149

Question 27 of 149

If ϵ,E\epsilon, E and tt represent the free space permittivity, electric field and time respectively, then the unit of ϵEt\frac{\epsilon E}{t} will be :

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Answer: (C) A/m2\mathrm{A} / \mathrm{m}^{2}

We need to find the unit of ϵEt\frac{\epsilon E}{t}.
From Maxwell's equations, the displacement current density is given by Jd=ϵ∂E∂tJ_d = \epsilon \frac{\partial E}{\partial t}.
The term ϵEt\frac{\epsilon E}{t} has the same dimensions as displacement current density JdJ_d.
Current density JJ is defined as current per unit area, J=IAJ = \frac{I}{A}.
The SI unit of current II is Ampere (A) and the SI unit of area AA is m2m^2.
Therefore, the unit of current density is A/m2A/m^2.
Alternatively, using dimensions:
[ϵ]=M−1L−3T4A2[\epsilon] = M^{-1}L^{-3}T^4A^2
[E]=MLT−3A−1[E] = MLT^{-3}A^{-1}
[t]=T[t] = T
Dimension of ϵEt=(M−1L−3T4A2)(MLT−3A−1)T=L−2A\frac{\epsilon E}{t} = \frac{(M^{-1}L^{-3}T^4A^2)(MLT^{-3}A^{-1})}{T} = L^{-2}A.
This corresponds to the unit A/m2A/m^2.

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