The Hall probe is then shifted away from the wire along line $XY$. On the axes in Fig. 5.2, sketch a graph to show how the Hall voltage $V_H$ changes with the probe distance $x$ from the wire. No numerical scale values are needed on your sketch.
The Hall probe is now put back at its initial position, a distance $d$ from the wire. At this location, the magnetic flux density produced by the current in the wire is proportional to the current. With a direct current of $4.0\,\text{A}$ in the wire, the Hall probe reading is $3.5\,\text{mV}$. The direct current is then changed to an alternating current with root-mean-square (r.m.s.) value $4.0\,\text{A}$. The period of this alternating current is $T$. On the axes of Fig. 5.3, sketch how the Hall voltage reading $V_H$ varies with time $t$ for two cycles of the alternating current. Include numerical values for $V_H$ where they are appropriate.
A student proposes replacing the Hall probe in (a) with a small coil connected in series with a millivoltmeter. The steady current in the wire is $4.0\,\text{A}$. To collect data for a graph showing how magnetic flux density varies with distance $x$, the student suggests taking millivoltmeter readings while the coil is held fixed at different values of $x$. Comment on this suggestion.