- 13

- 0

**1. The problem statement, all variables and given/known data**

When a wire carries an AC current with a known frequency you can use a Rogowski

coil to determine the amplitude Imax of the current without disconnecting the wire to

shunt the current in a meter. The Rogowski coil, shown in the ﬁgure, simply clips

around the wire. It consists of a toroidal conductor wrapped around a circular return

cord. The toroid has n turns per unit length and a cross-sectional area A. The current

to be measured is given by I(t) = Imax sin (ω t). (a) Show that the amplitude, E, of the

emf induced in the Rogowski coil is E = μ0 n A ω Imax. (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.

**2. Relevant equations**

Emf= -N(dI/dt) where I = magnetic flux, not current

Emf = I/R = R*(dQ/dt) where I = current

Magnetic flux = *integral* (B*dA)

Emf = *surface integral* (E*dL) = -(d*magnetic flux*/dt)

**3. The attempt at a solution**

I am not really sure where to start - maybe by using the Emf= I/R ?? Can anyone help get me started in the right direction? Thanks!