A uniform magnetic eld ~B lls an in nite cylinder of radius R. A metal rod of length L isplaced as shown in the gure. The magnitude B changes at a rate dB=dt.1 Find the electric eld ~E in the cylindrical region. Hint: To nd the direction of ~E think of the problem of a hypothetical uniform electric eld ~Ehyp lling an in nite cylinder. If ~Ehypvaries in time, how is the displacement current distributed? What hypothetical magneticeld ~Bhyp does this current generate? Finally, use the duality of Maxwell-
Faraday andAmpere-Maxwell equations, as we have done in class (the same equations have the samesolutions).You can use a di erent example based on the same equations have the same
solutions. We have seen a couple in class!