# What are some experiments verifying Maxwell's 4th equation?

Please give me the link to some paper, website or book that you know about which discusses in detail some experiments which quantitatively verify Maxwell's 4th equation, which is $$\quad \nabla\times{\bf B} = \frac{1}{ c^2}\frac{\partial{\bf E}}{\partial t} + \mu_0{\bf J}$$

I am specially interested in the case where the electric field is constant and where Maxwell's equation becomes

$$\quad \nabla\times{\bf B} = \mu_0{\bf J}.$$

• Raja, please check how the curvature of the wire and by this the acceleration of the charges induces the magnetic field. – HolgerFiedler Dec 3 '15 at 17:09

## 1 Answer

A permanent current flowing through an electrical coil produces a magnetic field inside the coil : this is a direct consequence of Maxwell's fourth equation.

• Yes. Thanks. But i am asking about the detailed analysis. I accept that current causes magnetism, and the magnetic fields curls around the wire, as seen in pictures where magnetic fillings form pattern around current carrying wires. But i don't find intuitive is the fact that the summation of magnetic field around a closed loop must always equal a given function of current., as stated by maxwell – Prem kumar Dec 3 '15 at 14:38
• All of us who routinely use electromagnets are scratching our heads - the resulting magnetic field clearly is (within hysteresis) a given function of current. What motivates this doubt? – Jon Custer Dec 3 '15 at 15:02
• Yes, from general experience we know that magnetic field is 'proportional' to the current. But it is not clear to me why for a current wire the line integral of magnetic field around every current element should be the same irrespective of how we twist the wire. For example the law holds even if i twist the wires however i desire. This is why i was asking for conforming experiments. It is interesting that biot savart's experiments conform Ampere's law for steady current. I am trying to understand why that is so right now. – Prem kumar Dec 5 '15 at 14:33