A thin slice of conducting material has its faces PQRS and VWXY normal to a uniform magnetic field of flux density B, as shown in Fig. 9.1.

Question 10

A thin slice of conducting material has its faces PQRS and VWXY normal to a uniform magnetic field of flux density B, as shown in Fig. 9.1.

Fig. 9.1

Electrons enter the slice at right-angles to face SRXY.

A potential difference, the Hall voltage VH, is developed between two faces of the slice.

(a) (i) Use letters from Fig. 9.1 to name the two faces between which the Hall voltage is

developed. [1]

(ii) State and explain which of the two faces named in (a)(i) is the more positive. [2]

(b) The Hall voltage VH is given by the expression

VH = BI / ntq.

(i) Use the letters in Fig. 9.1 to identify the distance t. [1]

(ii) State the meaning of the symbol n. [1]

(iii) State and explain the effect, if any, on the polarity of the Hall voltage when negative

charge carriers (electrons) are replaced with positive charge carriers, moving in the same direction towards the slice. [2]

[Total: 7]

Reference: Past Exam Paper – March 2018 Paper 42 Q9

Solution:

(a) (i) PSYV and QRXW

{The Hall voltage developed should be developed on the faces perpendicular to both the magnetic field and the direction of motion of the electrons.}

(ii)

electron moving in magnetic field deflected towards face QRXW

so face PSYV is more positive

{The direction of the force on the electrons can be determined from Fleming’s left hand rule.

Forefinger: field – downwards

Middle finger: current – to the right (opposite to the flow of electrons)

Thumb: force – towards QRXW

The electrons flow towards face QRXW. So, face QRXW becomes more negative while face PSYV becomes more positive.}

(b)

(i) PV or SY or RX or QW

{t is the thickness of the slice.}

(ii) number of charge carriers per unit volume

(iii)

Negative and positive charge (carriers) would deflect in opposite directions. So no change in polarity.

{A positive charge carrier would deflects towards face PSYV, again making it more positive.}