Chapter 31, Problem 31.18P

When a wire carries an AC current with a known frequency, you can use a Rogowski coil to determine the amplitude I_max of the current without disconnecting the wire to shunt the current through a meter. The Rogowski coil, shown in Figure P30.8, simply clips around the wire. It consists of a toroidal conductor wrapped around a circular return cord. Let n represent the number of turns in the toroid per unit distance along it. Let A represent the cross-sectional area of the toroid. Let I(t) = I_max sin ωt represent the current to be measured. (a) Show that the amplitude of the emf induced in the Rogowski coil is ${\mathcal{E}}_{\max }={\mu }_{0}nA\omega I_{\max }$. (b) Explain why the wire carrying the unknown current need not be at the center of the Rogowski coil and why the coil will not respond to nearby currents that it does not enclose.

Figure P30.8