A rod made of conducting material is in a region of uniform magnetic field. It is moved horizontally along two parallel conducting rails X and Y. The other ends of the rails are connected by a thin conducting wire.

The speed of the rod is constant and is also at right angles to the direction of the uniform magnetic field.

(i) Describe, with reference to the forces acting on the conduction electrons in the rod, how an emf is induced in the rod.

(ii) An induced emf is produced by a rate of change of flux. State what is meant by a rate of change of flux in this situation.

The length of the rod in (a) is 1.2 m and its speed is 6.2 m s^–1. The induced emf is 15 mV.

(i) Determine the magnitude of the magnetic field strength through which the rod is moving.

(ii) Explain how Lenz’s law relates to the situation described in (a).

(i) electrons are moving at right angles to the magnetic field;
electrons experience a force directed along the rod / charge is separated in the rod;
the work done by this force to achieve this separation leads to an induced
emf; 

(ii) the product of magnitude of field strength and the rate at which the area is swept out by the rod is changing / the rate at which the rod cuts through field lines;

(i) \(B = \frac{\varepsilon }{{vl}}\);
(must see the data book equation re-arranged or correctly aligning substitution with equation)

\( = \left({\frac{{15 \times {{10}^{ - 3}}}}{{6.2 \times 1.2}} = } \right)2.0{\rm{mT}}\); (accept 2+sf)
To award [2] both steps must be seen.

(ii) Lenz’s law states that the direction of the induced emf/current is such as to oppose the change producing it;
there is a current in the rod due to the induced emf;
the force on the current/rod due to the magnetic field is in the opposite direction to the force producing the motion of the rod;

It continues to be apparent that candidates find this a difficult area of the syllabus in which a clear and unshakeable understanding of the concepts is required.

(i) A good number did not consider the forces acting on the electrons as instructed and therefore gained few, if any, marks. Of the remainder, some were able to discuss the forced motion of the electrons in the field and how this leads to the direction of the forces on the electrons along the rod. It was rare to see a consideration of the connection between the work done on the electrons and the emf itself.

(ii) Only a few candidates could adequately explain what is meant by a rate of change of flux. The “rate of change” aspect was usually missing.

(i) The calculation of magnetic field strength followed directly from a substitution into a Data Booklet equation and so was often well done apart from the inevitable power of ten errors by those who forgot the “m” in “mV”.

(ii) This was very poor indeed. Many could not even state Lenz‟s law adequately and could get no further. It was rare to see a good link made between the law itself and the induced current in the circuit.