Physics 9702 · AS & A Level · Force on a moving charge
Force on a moving charge — practice question
A narrow slab of conducting material is positioned at right angles to a uniform magnetic field of flux density $B$, as shown in Fig. 8.1. The magnetic field is at right angles to face CDEF and to face PQRS. A current $I$ flows through the slab and is at right angles to faces CDQP and FERS. A potential difference, the Hall voltage $V_H$, is produced across the slab.
(a)[1]
State the faces across which the Hall voltage $V_H$ is developed.
(b(i))[3]
The current $I$ is carried by charge carriers, each with charge $+q$ and moving at speed $v$ in the direction of the current. The number density of the charge carriers is $n$. Derive an expression connecting the Hall voltage $V_H$ with $v$, $B$ and $d$, where $d$ is one of the dimensions of the slice.
(b(ii))[2]
Use your answer from (b)(i) together with an expression for the current $I$ in the slice to derive $V_H = \frac{BI}{ntq}$. Show your working.
(c)[2]
Suggest why the Hall voltage is hard to detect in a thin slice of copper.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “CFSP and DERQ” …