Frustrated by the small Hall voltage obtained in blood flow measurements, a medical physicist decides to increase the applied magnetic field strength to get a\({\rm{0}}{\rm{.500}}\;{\rm{V}}\)output for blood moving at\({\rm{30}}{\rm{.0 cm/s}}\)in a\({\rm{1}}{\rm{.50}}\;{\rm{cm}}\)diameter vessel. (a) What magnetic field strength is needed? (b) What is unreasonable about this result? (c) Which premise is responsible?

• Hall voltage is\({\rm{0}}{\rm{.500 V}}\)
• The velocity of blood is 30.0 cm/s
• Diameter of the vessel is\(1.50\;{\rm{cm}}\)

When a current-carrying conductor is placed in a magnetic field that is perpendicular to the direction of the flow of current, a transverse electric field develops in the conductor. This phenomenon is known as the Hall effect.

(a)

\(\varepsilon = vlB\).

Then solving this equation using the given values to evaluate for the strength of the magnetic field.

\(\begin{aligned}{}B &= \frac{\varepsilon }{{vl}}\\ &= \frac{{0.500 {\rm{V}}}}{{0.015 {\rm{m}} \times 0.30 {\rm{m/s}}}}\\ &= 111\; {\rm{T}}\end{aligned}\)

Therefore, the magnetic field strength is: \({\rm{111 T}}\).

(b) The magnetic field evaluated is too strong to be practically achieved.

(c) The value of hall voltage, \({\rm{0}}{\rm{.5 V}}\) is too large.