If denotes the permittivity of free space and is the flux of the electric field through the area bounded by the closed surface, then dimension of are that of: [2025]

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Solution

Q.
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 dimension of $(ε_{0} \frac{d ϕ_{E}}{d t})$ are that of: [2025]

1 Electric field

2 Electric potential

3 Electric charge

4 Electric current

Ans.
(4)

We know that formula for displacement current is given by

$i_{d} = ε_{0} \frac{d ϕ_{ε}}{d t}$

Dimension of $ε_{0} (\frac{d ϕ_{E}}{d t})$ will be

Same as electric current

So $[ε_{0} \frac{d ϕ_{E}}{d t}] = A$

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