A uniform magnetic field perpendicular to a thin rectangular aluminium sheet varies sinusoidally with time. The sheet is 0.50 mm thick.
(i) For a 1.0 cm × 1.0 cm square element of the sheet, the peak magnetic field is 0.12 T and the frequency is 2.0 kHz. Calculate the rms emf induced around the perimeter of the square element.
(ii) The effective length of the eddy current path around the square may be taken as 4.0 cm. Given the resistivity of aluminium is 2.8×10−8Ω m, find the rms eddy current in the loop.
(iii) Hence compute the average power dissipated as heat in this element.
(iv) If the frequency is increased to 4.0 kHz while the peak magnetic field remains 0.12 T, by what factor will the average power in the element change?