Electric Field induced by a Magnetic Field inside a Solenoid

[shj]

 

[Charles Link]

The integral around the loop does not obey $\frac{d \mathcal{E}}{ds}=E$. (What you did works for $F(x)=\int\limits_{a}^{x} f(t) \, dt$. Then $\frac{dF(x)}{dx}=f(x)$. This loop integral does not have this form). Instead, the integral is evaluated as $\mathcal{E}=(E)(2 \pi r)=\pi r^2 |\frac{dB}{dt}|$

 

[shj]

The integral around the loop does not obey $\frac{d \mathcal{E}}{ds}=E$. (What you did works for $F(x)=\int\limits_{a}^{x} f(t) \, dt$. Then $\frac{dF(x)}{dx}=f(x)$. This loop integral does not have this form). Instead, the integral is evaluated as $\mathcal{E}=(E)(2 \pi r)=\pi r^2 |\frac{dB}{dt}|$

alright