Example 22.3 from College Physics, 22.6 The Hall Effect

Calculating the Hall emf: Hall Effect for Blood Flow

A Hall effect flow probe is placed on an artery, applying a 0.100-T magnetic field across it, in a setup similar to that in Figure 22.29. What is the Hall emf, given the vessel’s inside diameter is 4.00 mm and the average blood velocity is 20.0 cm/s?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
Because $B$ , $v$ , and $l$ are mutually perpendicular, the equation $ε = Blv$ can be used to find $ε$ .
Solution
Entering the given values for $B$ , $v$ , and $l$ gives
$\begin{array}{l} ε & = & Blv = (0.100 T) (4 . 00 \times 10^{- 3} m) (0 .200 m/s) \\ = & 80.0 μV \end{array}$
22.14
Discussion
This is the average voltage output. Instantaneous voltage varies with pulsating blood flow. The voltage is small in this type of measurement. $ε$ is particularly difficult to measure, because there are voltages associated with heart action (ECG voltages) that are on the order of millivolts. In practice, this difficulty is overcome by applying an AC magnetic field, so that the Hall emf is AC with the same frequency. An amplifier can be very selective in picking out only the appropriate frequency, eliminating signals and noise at other frequencies.

0 of 3 steps open

How did it go?

Strategy

Solution

Discussion

Strategy

Solution

Discussion