A large water main is \({\rm{2}}{\rm{.50 m}}\) in diameter and the average water velocity is\({\rm{6}}{\rm{.00}}\;{{\bf{m}} \mathord{\left/ {\vphantom {{\bf{m}} {\bf{s}}}} \right. \\} {\bf{s}}}\).Find the Hall voltage produced if the pipe runs perpendicular to the Earth’s \({\rm{5}}{\rm{.00 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{ - T}}\) field.

The diameter of the large water main is\(L{\bf{ = }}2.{\bf{50}}\;m\)\(\)

The magnetic field strength of the earth is\({\bf{B = 5}}{\bf{.00}} \times {10^{ - 5}}\;{\bf{T}}\)

The speed of the aluminum rod is \({\bf{v = }}6.{\bf{00}}\;{{\bf{m}} \mathord{\left/ {\vphantom {{\bf{m}} {\bf{s}}}} \right. \\} {\bf{s}}}\)

The Hall effect defines the generation of induced voltage due to the motion of charge carriers in a perpendicular applied magnetic field and can be defined as,

\({\bf{E = BLv}}\)…………………(1)

Substitute the given data in equation (1), which will result,

\({\rm{E}} = {\rm{BLv}}\)

\( = \left( {{\rm{5}}{\rm{.00}} \times {\rm{1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{T}}} \right) \times \left( {{\rm{2}}{\rm{.50 m}}} \right) \times \left( {{\rm{6}}{\rm{.00 }}{{\rm{m}} \mathord{\left/ {\vphantom {{\rm{m}} {\rm{s}}}} \right. \\} {\rm{s}}}} \right)\)

\( = {\rm{7}}{\rm{.50}} \times {\rm{1}}{{\rm{0}}^{{\rm{ - 4}}}}\;{\rm{V}}\)

Therefore, the induced hall voltage is \({\rm{7}}{\rm{.50}} \times {\rm{1}}{{\rm{0}}^{{\rm{ - 4}}}}\;{\rm{V}}\).