Question

a circular coil of radius 0.11m contains a single turn and is located in a constant magnetic field of magnitude 0.27T. the magnetic field has the same direction as the normal to the plane of the coil. the radius increase to 0.3m in a time of 0.08s.
a) Determine the magnitude of the emf induced in the coil
b) The coil has resistance of 0.7ohm. Find the magnitude of induced current.

Answer 1

Faraday's Law of Electromagnetic Induction states that \[emf = - N (\Delta \Phi) / (\Delta t) \]N refers to the number of turns; it is given that N = 1.
Phi refers to the change in magnetic flux and is equal to \[\Phi=BAcos \theta\]where theta refers to the angle between the direction of the magnetic field and the normal to the plane of the coil. It is given that both point in the same direction, so theta = 0.
The magnetic flux is changing because the area is changing (while the magnetic field strength remains constant; B = 0.27 T). So the change in magnetic flux is \[\Delta \Phi=B \Delta A \cos \theta=B \Delta A\]You can easily find the change in area by noting that the radius is changing and that\[A = \pi \times r ^{2}\]It is also given that the change in time is 0.08s. So the magnitude of the emf will be\[emf = \left| - (B \Delta A)/(\Delta t) \right|\]Once you determine the induced emf (which is equivalent to voltage), you can easily find induced current since Ohm's Law states that \[V = IR\] It is given that R = 0.7 ohms. V = induced emf. Therefore,\[I = V/R\]