Maxwell’s Equations – Differential form of Faraday’s law (Part 6)



This is Part six of my eight part series on Maxwell Equations

I had already covered Gauss’s law for electric field in two articles and links to both these articles are

  1. Maxwell’s Equations – Integral form of Gauss’s Law (Part 1)
  2. Maxwell’s Equations – Differential form of Gauss’s Law (Part 2)

Previous two articles in this series were about Gauss’s Law for magnetic fields and their links are

  1. Maxwell’s Equations – Integral form of Gauss’s Law for magnetic fields(Part 3)
  2. Maxwell’s Equations – Differential form of Gauss’s Law For Magnetic Field(Part 4)

My last article in this series was about Integral form of Faraday’s law and this article is about Differential form of Faraday’s Law.

Faraday’s Law in differential form is written as
\overrightarrow \nabla \times \overrightarrow E = - \frac{{\partial \vec B}}{{\partial t}}

From the left side of the equation is nothing but the curl of the electric field and it tells about the tendency of field lines to circulate around a point . Curl of a vector means how much the vector curls around the point in question. The right side represents the rate of change of magnetic field with time. So from this it could be stated that

A circulating electric field is produced by a magnetic field that changes with time.

Now I’ll try to explain the meaning of each and every symbol used in integral form of Faraday’s law by first considering the left hand side of the equation

  1. \vec \nabla  \times \vec E : here  \vec \nabla  is a differential vector operator and the cross product turns the del operator into the curl and  \vec E is electric field measured in V/m. The curl of a vector field is a measure of the field’s tendency to circulate about a point – much like the divergence is a measure of the tendency of the field to flow away from a point. Now when we talk about point charges electric fields diverge away from points of positive charge and converge toward points of negative charge, such fields cannot circulate back on themselves. So what kind of fields circulates back on themselves? Electric fields induced by changing magnetic fields are different. Wherever a changing magnetic field exists, a circulating electric field is induced. Unlike charge-based electric fields, induced fields have no origination or termination points – they are
    continuous and circulate back on themselves.
  2. \frac{\partial B }{\partial t} : is the rate of change of magnetic field with time

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