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: VH
= 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.
VH is proportional
to B and B is inversely proportional to the distance x.
So, VH 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: VH
= 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 × Irms
Peak voltage V0
= √2 × Vrms
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.}
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