A long cylindrical wire carrying a constant current I has a small gap as shown in the figure below. The faces of the gap act as capacitor plates and charge accumulates on them. Two circular loops, one around the wire and one around the gap, are used in Amp�re's law. No current cuts through the interior of loop 2, but electric field lines in the gap do cut through it. As the electric field in the gap increases in magnitude, the electric flux through the interior of loop 2 increases.
Apply the Amp�re-Maxwell law to one of the circular paths in the figure below to find the magnitude B of the magnetic field outside the gap in the wire at a distance r ? R from the central axis. [Hint: What is the rate of change of electric flux through the circle in terms of the current I?] (Use any variable or symbol stated above along with the following as necessary: ?0.)