A uniform magnetic field B exists in a cylindrical region, indicated by the dotted line in the figure. The magnetic field increases at a constant rate dB dt . Consider a circle of radius r coaxial with the cylindrical region. Determine the magnitude of the electric field E at a point on the circumference of the circle.

Step-by-step solution

According to Faraday's law of electromagnetic induction, the magnitude of the induced electromotive force in a closed loop is equal to the rate of change of magnetic flux through it: E d l = | d dt | For a circle of radius r coaxial with the cylindrical region, the magnetic flux enclosed is: = B r^2 The rate of change of magnetic flux is: | d dt | = r^2 dB dt Due to the cylindrical symmetry of the magnetic field, the induced electric field E is tangential to the circle and its magnitude is constant everywhere on th