Q18: When a wire carries an AC current with a known fre- quency, 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 P31.18, 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) 5 I max sin vt represent the current to be measured.
(a) Show that the amplitude of the emf induced in the Rogowski coil is e max 5 m0nAvI max.
(b) Explain why the wire carrying the unknown cur- rent 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.