$11.2.2$ The induction of a uniform magnetic field inside a cylinder of radius $r$ = 0.1 m increases linearly with time: $B = \alpha t$ (coefficient $\alpha$ = 10$^{-3}$ T/s). The magnetic field is directed along the axis of the cylinder. What is the strength of the eddy electric field at a distance of $l$ = 0.2 m from the cylinder axis?
Magnetic field passes through an area of $\pi r^2$ m$^2$ and its flux increases with time. So, this causes that appears a rotational electric field around cylinder axis such that its induced magnetic field opposes to $\vec{B}(t)$ (Lenz Law). Applying Faraday's Law, $$\oint\vec{E}\cdot \vec{ds} = \frac{d\Phi_B}{dt}$$ this closed integral is for concentric circular paths about cylinder's axis. Then, for a distance $a$ from center, $$E(a) \cdot 2\pi a = \pi r^2 \alpha$$ $$E(a) = \frac{\alpha r^2}{2a}$$ Finally, evaluating for $a=l$, $$E = \frac{\alpha r^2}{2l}$$
$$E = 2.5~\cdot~10^{-5}~{\rm{\frac{V}{m}}}$$