A Hall probe is placed a distance d from a long straight current-carrying wire, as illustrated in Fig. 5.1.

Question 11

A Hall probe is placed a distance d from a long straight current-carrying wire, as illustrated in Fig. 5.1.

Fig. 5.1

The direct current in the wire is 4.0 A. Line XY is normal to the wire.

The Hall probe is rotated about the line XY to the position where the reading VH of the Hall probe is maximum.

(a) The Hall probe is now moved away from the wire, along the line XY.

On the axes of Fig. 5.2, sketch a graph to show the variation of the Hall voltage VH with

distance x of the probe from the wire. Numerical values are not required on your sketch.

Fig. 5.2

[2]

(b) The Hall probe is now returned to its original position, a distance d from the wire.

At this point, the magnetic flux density due to the current in the wire is proportional to the

current.

For a direct current of 4.0 A in the wire, the reading of the Hall probe is 3.5 mV.

The direct current is now replaced by an alternating current of root-mean-square (r.m.s.)

value 4.0 A. The period of this alternating current is T.

On the axes of Fig. 5.3, sketch the variation with time t of the reading of the Hall voltage VH for two cycles of the alternating current. Give numerical values for VH, where appropriate.

Fig. 5.3

[3]

(c) A student suggests that the Hall probe in (a) is replaced with a small coil connected in series with a millivoltmeter. The constant current in the wire is 4.0 A.

In order to obtain data to plot a graph showing the variation with distance x of the magnetic flux density, the student suggests that readings of the millivoltmeter are taken when the coil is held in position at different values of x.

Comment on this suggestion. [2]

Reference: Past Exam Paper – June 2014 Paper 42 Q5

Solution:

(a)

The graph is only a curve with a decreasing gradient.

{Hall voltage: V_H = BI / ntq

The Hall voltage is proportional to the magnetic field strength B.

B = μ₀I / 2πx

where B is the magnetic field strength at distance x from the centre of the wire,

I is the current and

μ₀ is the magnetic field constant.

V_H is proportional to B and B is inversely proportional to the distance x.

So, V_H is inversely proportional to x.

The Hall probe was initially placed at x =d and moved away. So, the curve should start at x = d.}

(b)

For the graph, from time = 0 to time = 2T, there are 2 cycles of a sinusoidal wave.

The peaks are at 4.95 mV / 5.0 mV

{ Hall voltage: V_H = BI / ntq

The Hall voltage is proportional to the current I.

An r.m.s. value of current produces a voltage of 3.5 mV.

Peak current I₀ = √2 × I_rms

Peak voltage V₀ = √2 × V_rms

peak voltage = √2 × 3.5 = 4.9 5mV}

(c) An e.m.f. is induced in the coil when the magnetic field / flux is changing / cutting.  At each position, the magnetic field does not vary, so no e.m.f. is induced in the coil / no reading on the millivoltmeter

{An emf is induced when there is a CHANGE in the magnetic flux.}