If ϵ_0 denotes the permittivity of free space and _E is the flux of the electric field through the area bounded by the closed surface, then dimensions of ( ϵ_0 d _E dt ) are that of:

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Accepted Answer

Correct answer: C. (c) We can use Gauss's law to analyze the dimensions. Gauss's law states that _E= qϵ_0, where _E is the electric flux, q is the electric charge, ϵ_0 is the permittivity of free space. To find the dimensions of ϵ_0 d _E dt, follow these steps: Differentiate Gauss's law with respect to time: d _E dt= 1ϵ_0 dq dt . Multiply the equation by ϵ_0 : ϵ_0 d _E dt= dq dt . Recognize that the time rate of change of charge, dq dt, is by definition the electric current. Thus, the dimensions of ϵ_0 d _E dt are those of electric current.

$If ϵ_{0} denotes the permittivity of free space and Φ_{E} is the flux of the electric field through the area bounded by the closed surface, then dimensions of (ϵ_{0} \frac{d φ _{E}}{dt}) are that of:$

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