# What is the self-induced electromotive force of this coil?

Coil length $$l=1m$$, its wire length $$l'=10m$$, current intensity that passes in it $$i = 5-2t$$. This is all the given information.

I tried this:

$$N$$ is number of loops in the coil, $$s$$ is the area of the coil

$$\displaystyle \epsilon = -\frac{\Delta \Phi}{\Delta t}$$

$$\Delta \Phi = N \cdot \Delta B \cdot s$$

$$\displaystyle \Delta B = 4\pi \times 10^{-7}\frac{N \cdot \Delta i}{l}$$

$$\displaystyle N = \frac{l'}{2\pi r}$$ , $$s = \pi r^2$$

$$\displaystyle \Delta \Phi = 4\pi \times 10^{-7} \frac{(\frac{l'}{2\pi r})^{2}\cdot \pi r^2}{l} \cdot \Delta i$$

$$\displaystyle \Delta \Phi = 10^{-7} \frac{l'^{2}}{l}\cdot \Delta i = 10^{-5}\cdot \Delta i$$

$$\Delta i = 5-2\Delta t \Longrightarrow \Delta \Phi = (5-2\Delta t)\times 10^{-5}$$

$$\displaystyle \epsilon = -\frac{(5-2\Delta t)\times 10^{-5}}{\Delta t}$$

Is that it, am I done? or did I make a mistake somewhere?