| Date | November 2011 | Marks available | 4 | Reference code | 11N.2.HL.TZ0.7 |
| Level | Higher level | Paper | Paper 2 | Time zone | Time zone 0 |
| Command term | Determine | Question number | 7 | Adapted from | N/A |
Question
Part 2 Electromagnetic induction
The diagram shows a horizontal metal rod suspended by two vertical insulated springs.
The rod moves vertically up and down with simple harmonic motion with a time period T at right angles to a uniform magnetic field.
The diagram shows the variation with time t of the vertical displacement x of the rod.
On the axes provided, draw a graph to show
(i) the variation with time t of the vertical velocity v of the rod.
(ii) the variation with time t of the emf generated between the ends of the rod.
The length of the rod is 0.18 m and the magnitude of the magnetic field is 58 μT. The frequency of the simple harmonic motion is 2.5 Hz. The amplitude of the motion is 8.2×10-2 m.
Determine the magnitude of the maximum emf εmax between the ends of the rod.
The frequency of the motion is doubled without any change in the amplitude of the motion.
State and explain the changes to the variation with time t of the emf \(\varepsilon \) generated as a result of this change in frequency.
Markscheme
(i)
cosine wave same frequency as original;
phase correct;
(ii) emf in phase or antiphase with answer to (a)(i);
max speed =8.2×10-2×2π×2.5(=1.29ms-1);
ε=58×10-6×0.18×1.29;
13.5 μV;
frequency of the emf doubles / period halves;
because same change of flux in half the time / because frequency of emf must equal frequency of oscillation;
maximum emf doubles;
maximum speed doubles / flux changes at twice rate;
