# Justifying Ampere's Law and Faradays Law with an experiment

1. Apr 1, 2016

### PhotonSSBM

1. The problem statement, all variables and given/known data
Given Ampere's Law and Faraday's Law (in differential or integral form fwiw) explain why it is easier to design an experiment to show that a changing magnetic field creates an electric field than it is to show a changing electric field creates a magnetic field. Justify your answer with numbers.

2. Relevant equations
$\nabla x \vec{B} = \mu_0\vec{J} + \mu_0\epsilon_0\frac{d\vec{E}}{dt}$
$\nabla x \vec{E} = \frac{-d\vec{B}}{dt}$

3. The attempt at a solution
So this was from an exam I just took. I beat my head against it for about 45 minutes and could only really come up with this:

For Faraday's law, it only requires that a changing magnetic field be present. This can be accomplished easily by simply moving a magnet around a conductor, since if an electric field is created, the electrons in the conductor will move, and we can see the effects of this in a coil of wire with a segment cut out. As the magnet moves sparks of current should be visible at that cut out.

For Ampere's Law however it is hard to create a changing electric field independent of current (where $\vec{J} = \vec{0}$). One would need to create a changing electric field that propagates through free space and measure the magnetic effects on objects as a result, which would have been challenging without tools that can properly control photons.

I honestly just didn't know how to describe the difficulties of Ampere's Law better than this. And I didn't have time to think of any numerical justifications for my arguments since the other 3 problems also took about 45 minutes a piece. How would you have gone about answering this differently?

2. Apr 1, 2016

### Simon Bridge

Hard to change the electric field without moving charges about yes.