A cylindrical iron rod of infinite length with cross-sectional area A is oriente

Question

A cylindrical iron rod of infinite length with cross-sectional area A is oriented with its axis of symmetry coincident with the z axis of a cylindrical coordinate system as shown in the figure. It has a magnetic field inside that varies according to Bz(t)=B0+B1t. Find the theta component E?(R,t) of the electric field at distance R from the z axis, where R is larger than the radius of the rod. (Figure 2)

Express your answer in terms of A, B0, B1, R, and any needed constants such as ?0,?, and ?0.

Explanation / Answer

Faradays Lay = d(flux)/dt = E.(2pi*R)

flux = integral B.dA = (B0 + B1t)(A)

Hence , d(flux)/dt = B1A

B1A = (2pi*R)E

E = B1A/ (2pi*R)

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