# The inconsistency of continuity equation for time varying fields was corrected by Maxwell and the correction applied was

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The inconsistency of continuity equation for time varying fields was corrected by Maxwell and the correction applied was
1. Ampere's law, $\frac{{\delta D}}{{\delta t}}$
2. Gauss's law, J
3. Faraday's law, $\frac{{\delta B}}{{\delta t}}$
4. Ampere's law,$\frac{{\delta P}}{{\delta t}}$

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Correct Answer - Option 1 : Ampere's law, $\frac{{\delta D}}{{\delta t}}$

Amperes law:

The line integral of the magnetic field around any closed curve is equal to μ0 times the net current I threading through the area enclosed by the curve.

$\oint \vec B \cdot \overrightarrow {dl} = {\mu _0}I$

Modified Ampere's Law:

• To modify Ampere’s law, Maxwell followed a symmetry consideration, i.e. by Faraday’s law, a changing magnetic field induces an electric field, hence a changing electric field must induce a magnetic field.
• As currents are the usual sources of the magnetic field, a changing electric field must be associated with the current. Maxwell called that current as displacement current.
• To maintain the dimensional consistency, the displacement current is added in ampere’s law.

$\oint \vec B \cdot \overrightarrow {dl} = {\mu _0}I + {\mu _0}{\epsilon_0}\left( {\frac{{d{{\rm{E}}}}}{{dt}}} \right)$

$\oint \vec B \cdot \overrightarrow {dl} = {\mu _0}I + {\mu _0}{}\left( {\frac{{d{{\rm{D}}}}}{{dt}}} \right)$

The inconsistency of continuity equation for time varying fields was corrected by Maxwell and the correction applied was

$\left( {\frac{{d{{\rm{D}}}}}{{dt}}} \right)$

Gauss' Law:

1) This law gives the relation between the distribution of electric charge and the resulting electric field.

2) According to this law, the total charge Q enclosed in a closed surface is proportional to the total flux ϕ  enclosed by the surface.

ϕ α Q

3) The Gauss law formula is expressed by

ϕ = Q / ϵ0

$\oint \vec E \cdot \overrightarrow {dA}=Q/\epsilon_0$