A loop of copper wire in a region of uniform magnetic field is rotated about a horizontal axis.

The magnitude of the magnetic field strength is B and the area of the loop is A.

(i) State the minimum value and the maximum value of the magnetic flux linking the loop.

(ii) Outline with reference to Faraday’s law why, if the speed of rotation of the loop is increased, the maximum emf induced in the loop is increased.

The loop in (a) is connected in series with a resistor of resistance 15 Ω. The root mean squared (rms) value of the sinusoidal current in the resistor is 2.3 mA.

(i) Explain what is meant by the rms value of a sinusoidal current.

(ii) Determine the maximum power dissipated in the resistor.

(i) minimum: zero / –BA (minus sign required)
maximum: BA } (both needed)

(ii) Look for these main points:
(Faraday’s law states that the) induced emf equals/is proportional to the rate of change of flux/flux linkage; { (must see induced)
speed greater so time for change shorter / flux (linkage) is unchanged;
greater rate of change (of flux etc) gives a greater (induced) emf;
Award [1 max] if answer states flux (linkage) change is larger.

(i) (equivalent) direct current;
dissipating same power in a (fixed) resistor (as the rms current);

(ii) maximum current \( = \left( {\sqrt 2  \times 2.3 = } \right)3.2/3.3{\rm{mA}}\);
maximum power = (3.3²×15=)0.16mW;