I Faraday's Law Equation: Derivative vs Delta

I
Thread starter ManfredArcane
Start date Dec 3, 2022
Tags

Faraday's law Law

AI Thread Summary

The discussion centers on the two forms of Faraday's Law: ε=-(dΦB)/(dt) and ε=-(ΔΦB)/(Δt). The first equation represents the instantaneous rate of change of magnetic flux, while the second is an approximation used when the change is relatively constant over a time interval. Both forms are considered equivalent under specific conditions, particularly when the rate of change is stable. The approximation is useful for practical calculations in scenarios where precision is less critical. Understanding these nuances is essential for applying Faraday's Law effectively in physics.

Dec 3, 2022

ManfredArcane

My textbook gives the equation for Faraday's Law as ε=-(dΦ_B)/(dt) , the derivative of magnetic flux with respect to time. I have also seen Faraday's law expressed as ε= -(ΔΦ_B)/(Δt). Are these two forms equivalent? Thanks!

Physics news on Phys.org

Dec 3, 2022

anuttarasammyak

Gold Member

You can take them equivalent.

Dec 4, 2022

Ibix

Science Advisor

Insights Author

The latter is an approximation to the former. It's only valid when the rate of change is constant, or close enough that you don't care.

Thread 'Free surface problem in electrohydrodynamics'

I'm thinking about the following problem. I have an electrified fluid with a constant charge density, Q, within the fluid. Will this necessarily yield a surface charge? Would I have to compute it by looking at the displacement fields on either side of the interface? Would it change if the bulk charge within the fluid remains constant?

View full post »

Thread 'Maxwell stress tensor'

This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...

View full post »

Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'

Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...

View full post »