A circular wheel of radius 10.0 cm is shown in the figure. Its upper half, depicted in dark, is made of iron, while the lower half is of wood. An iron rod connects the two junctions. A uniform magnetic field B of magnitude 2.00 10⁻⁴ T exists in the region above the central line, as suggested by the figure. The wheel is set into pure rolling on a horizontal surface. Determine the average emf induced during this period

Step-by-step solution

The iron part of the wheel forms a closed semicircular conducting loop of area A = 1 2 r^2 . Initially, this loop is in the upper half where the magnetic field B is present. The initial magnetic flux through the loop is: _i = B A = 1 2 B r^2 After t = 2.00 s , the iron part moves to the lower half where the magnetic field is zero. The final magnetic flux through the loop is: _f = 0 The magnitude of the average induced emf is given by Faraday's law: e_ avg = | t | = _i - _f t Substituting r = 0.1 m , B = 2.00 10⁻⁴ T