Units & Dimensions

JEE Main level, single correct, medium

87 of 149

Question 87 of 149

Which of the following physical quantities have the same dimensions?

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Answer: (A) Electric displacement (D⃗)\left(\vec{D}\right) and surface charge density

Electric displacement
D⃗=ϵ0E⃗\vec{D}={ϵ}_{0}\vec{E}
[D]=[ϵ0E]=[ϵ0σϵ0]\left[D\right]=\left[{ϵ}_{0}E\right]=\left[{ϵ}_{0}\dfrac{\sigma }{{ϵ}_{0}}\right]
[D]=[σ]\left[D\right]=\left[\sigma \right]
And surface charge density =σ=\sigma.
Thus, electric displacement (D)\left(D\right) and surface charge density have same dimension.

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