Faraday's Law of Induction — Question 1

Question 1

A tilted pickup responds to the changing normal component of the field

A fixed 60-turn coil of area .0120 square metre has its normal at 60 degrees to a uniform field. The field increases from .100 T to .400 T in .0500 s. Positive circulation follows the right-hand rule about the chosen normal.

1. Find the signed average emf.

2. Find the charge through a 9.00-ohm resistive circuit during the ramp; neglect self-inductance.

Question 1 - Solution

A tilted pickup responds to the changing normal component of the field

(a) Method and calculation

$$\Lambda=NAB\cos\theta,\quad\Delta\Lambda=60(.0120)(.300)\cos60^\circ=.108\,\mathrm{Wb}.$$$$\overline{\mathcal E}=-\Delta\Lambda/\Delta t=\boxed{-2.16\,\mathrm V}.$$

(b) Interpretation and further calculation

$$Q=\int i\,dt=\frac1R\int\mathcal E\,dt=-\Delta\Lambda/R.$$$$\boxed{Q=-.0120\,\mathrm C}.$$

Physical check

The sign refers to the specified normal and traversal; changing the chosen normal reverses both signed quantities.