A thin slice of conducting material is placed normal to a uniform magnetic field of flux density B, as shown in Fig. 8.1. [Figure 8.1] The magnetic field is normal to face CDEF and to face PQRS. A current I passes through the slice and is normal to the faces CDQP and FERS. A potential difference, the Hall voltage V_H, is developed across the slice.

1. (a)State the faces between which the Hall voltage V_H is developed.[1]
2. (b)(i)The current I is produced by charge carriers, each of charge +q moving at speed v in the direction of the current. The number density of the charge carriers is n. Derive an expression relating the Hall voltage V_H to v, B and d, where d is one of the dimensions of the slice.[3]
3. (b)(ii)Use your answer in (b)(i) and an expression for the current I in the slice to derive the expression V_H = BI / ntq. Explain your working.[2]
4. (c)Suggest why the Hall voltage is difficult to detect in a thin slice of copper.[2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.