Problem — Emf from a field B linear in time

Problem

A loop of area $S=0{,}02\ \text{m}^2$ is immersed in a field perpendicular to its plane that varies in time as $B(t)=4t$ tesla (with $t$ in seconds). Calculate the magnitude of the induced emf.

Solution

Flux as a function of time: $\Phi_B=B(t)\,S=4t\cdot 0{,}02=0{,}08\,t\ \ (\text{Wb})$

Induced emf (Faraday-Neumann-Lenz law): $\abs{\text{emf}}=\abs{\ddt{\Phi_B}}=0{,}08\ \text{V}=8\cdot 10^{-2}\ \text{V}$ $\ev{\abs{\text{emf}}=8\cdot 10^{-2}\ \text{V}}$

Links

Topics: Induzione elettromagnetica Concepts: Legge di Faraday-Neumann-Lenz · Flusso magnetico Skills: Bilancio di flusso