A bar magnet falls vertically from rest through a coil of wire. The potential difference (pd) across the coil is recorded by a datalogger.

The graph shows the variation with time of the pd across the coil.

(i) Explain, with reference to Faraday’s and Lenz’s laws, the shape of the graph.

(ii) The coil has 1500 turns. Calculate the magnitude of the maximum rate of change of magnetic flux.

The magnet is now suspended from a spring. The magnet is displaced vertically and starts to oscillate in and out of the coil. A sinusoidal alternating current of rms value 280 nA is induced in the coil.

(i) State in words how the rms value of the alternating current relates to a direct current of 280nA.

(ii) The coil has a resistance of 1.5MΩ. Calculate the peak voltage across the coil.

(iii) Explain what effect the generation of the current has on the oscillation of the magnet.

(i) rate of change of flux (linkage) leads to induced emf (Faraday);
direction of emf tends to oppose the change (Lenz);
thus emf in one direction as magnet enters and in the opposite direction as it leaves coil;
magnet going faster so second peak larger;
magnet going faster so width of second peak is less;

(ii) attempted use of \(\varepsilon  =  - N\frac{{\Delta \varphi }}{{\Delta t}}\);
recognition that the maximum pd is 0.8 (V);
\(\left( {\frac{{\Delta \varphi }}{{\Delta t}} =  - \frac{{0.8}}{{1500}} =  - } \right)5.3 \times {10^{ - 4}}\left( {{\rm{Wb}}{{\rm{s}}^{ - 1}}} \right)\);

(i) the value of the direct current (or voltage) that dissipates same power (in a resistor);
Do not allow \(\frac{{{I_0}}}{{\sqrt 2 }}\) etc.

(ii) I₀=396 (nA);
V₀=I₀R=0.59 (V);

(iii) damps oscillation / OWTTE;
dissipation of energy in coil/magnet;

(i) This was generally poorly answered, with candidates often failing to refer to Faraday’s and Lenz’s laws or the specifics of the graph.

(ii) Many candidates used the correct value for the potential difference but were unsure of the meaning of rate of change of magnetic flux; it was commonly believed that this was simply Φ which left candidates searching for a time value.

(i) The definition of the rms current in terms of the equivalent direct current was very poorly known and many simply said that it was the peak value divided by root 2.

(ii) Few managed to do this well with the most common (incorrect) answer being 0.42V.

(iii) Although many hinted at damping, few candidates overtly mentioned it or related it to the dissipation of energy in the coil.