# Investigating the relationship between a changing B field and the curl of the electric field induced

I am currently working on a 12 page lab report on Faraday's law, essentially investigating, how for different magnetic field strength through a stationary loop of wire with N number of turns, effects the corresponding curl of electric field induced. With the some context specified, what would be the measurable data required to calculate for the curl of the electric field. Yes I know I can calculate the curl easily by taking the partial time derivative of B... but I was hoping if anyone could asist me with the actual calculation for the $\nabla&space;\times&space;\vec{E}$... as to when I write it in matrix form: $$\begin{bmatrix} \hat{x} & \hat{y} &\hat{z} \\ \frac{\partial }{\partial x}& \frac{\partial }{\partial y} & \frac{\partial }{\partial z} \\ \vec{E_{x}}& \vec{E_{y}} & \vec{E_{z}} \end{bmatrix}$$ So from this matrix form... what measureable data can I collect from my experiment in order to calculate for the curl directly?

• It is difficult to measure induced electric field at a point. You would need several measurements close to each other in space to calculate curl of electric field. If you want to only verify Faraday's law, verify its integral version. Measure emf in a closed circuit and compare to rate of change of magnetic flux. The local version with curl is an extrapolation of this integral law to infinitesimally small loops. – Ján Lalinský Jul 28 at 22:07
• Given that it's quite difficult to calculate for the curl, directly with the cross product as it would require some difficult measurements... would there be any other methods to calculate for curl.... through the integral form that allow easy measurements? Cuz essentially I want to give a visual at the same time a mathematical representation of how electric field curl and therefore evaluate it's mathematical propertise in nature – EPIC Tube HD Jul 29 at 4:04
• The calculation is easy, what is difficult is to measure electric field with enough precision at two nearby points of space. There is no easier way to get curl than the above formula, any other way will need to measure electric field at two close points in space. – Ján Lalinský Jul 29 at 9:33
• @JánLalinský I'll try and think about the measurement bit.... but could you give me some example, if I were to measure for the curl using the cross product, how would I do it? If u could help me out with the individual measurable components for the curl that would be awesome! – EPIC Tube HD Jul 29 at 10:11
• You need to measure electric field at points of space with precisely known positions and then calculate curl by replacing derivatives by ratios. You can easily measure direction of (strong-enough) electric field with mosfets, but while measuring accurately field magnitude is possible, it is not an easy task. Read here about recent development in this area: phys.org/news/2018-01-sensor-electric-field-strength.html – Ján Lalinský Jul 31 at 0:12