(a) What is the speed of a supersonic aircraft with a$\mathbf{17}\mathbf{.}\mathbf{0}\mathbf{‐}\mathbf{m}$ wingspan, if it experiences a$\mathbf{1}\mathbf{.}\mathbf{60}\mathbf{‐}\mathbf{V}$ Hall voltage between its wing tips when in level flight over the north magnetic pole, where the Earth’s field strength is$\mathbf{8}\mathbf{.}\mathbf{00}\mathbf{\times }{\mathbf{10}}^{\mathbf{‐}\mathbf{5}}\mathbf{}\mathbf{T}$ (b) Explain why very little current flows as a result of this Hall voltage.

The wingspan of the supersonic aircraft is$\mathrm{L}=17.0\mathrm{m}$

The magnetic field strength of the earth is$\mathrm{B}=8.00\times {10}^{‐5}\mathrm{T}$

Induced voltage due to the Hall effect is$\mathrm{E}=1.60\mathrm{V}$

An induced voltage generated by a charge carrier moving in an applied magnetic field perpendicular to the direction of motion can be expressed as,

$\mathrm{E}=\mathrm{BLv}$ …………………(1)

Substitute the given data in equation (1) to evaluate the speed that produces such hall voltage can be given as,

$$\begin{gathered} \mathrm{v}=\frac{\mathrm{E}}{\mathrm{BL}} \\ =\frac{1.60\mathrm{V}}{\left(8.00\times {10}^{‐5}\mathrm{T}\right)\times \left(17.0\mathrm{m}\right)} \\ =1.17\times {10}^3\mathrm{m}/\mathrm{s} \end{gathered}$$

Therefore the speed of supersonic aircraft is $1.17\times {10}^3\mathrm{m}/\mathrm{s}$.

(b)

Very little current flows as a result of this Hall voltage due to the reason that there exists a magnetic force that pushes the charges in the opposite direction.

Therefore, the flow of a small current is due to the Hall voltage as there already exists a magnetic force pushing the charges in the opposite direction.