Hall Effect Probe for Measuring Magnetic Field Strength

[Angie K.]

Homework Statement

In a probe that uses the Hall effect to measure magnetic fields, a 11-A current passes through a 1.33-cm-wide and 1.31-mm-thick strip of sodium metal. If the Hall emf is 2.42 μV, what is the magnitude of the magnetic field (take it perpendicular to the flat face of the strip)? Assume one free electron per atom of Na, and take sodium's mass density to be 0.971 g/cm3.

The current density j (current per cross-sectional area) is given by j = nev, where n is the number density of free charges,e is the charge of an electron, and v is the drift velocity of the electrons. See Chapter 25, Section 25-8, for more details. Note that j = I/A, where A is the area perpendicular to the current flow, so from I/A = nev, you can find the drift velocity v.
•See the Periodic Table in the back cover of your book to find out the atomic weight of sodium.

Homework Equations

v = IB/n e d

The Attempt at a Solution

I figured the equation to be IB/n e d (from hint given in problem) but I am not sure how to calculate n e d. Is n, (number of atoms) of Na 23kg? then e is 1.6*10^-19 Coulombs and d is the width from the given variables. (1.33 cm)?

 

[Scott Redmond]

For n, that's not quite right. I would take a quick look at section 25-8 to see what you can find about n.

I would also suggest drawing a cross-sectional sketch that clearly shows the dimensions, the electric and magnetic field directions, and the electric and magnetic force directions. Ideally, you would use your diagram, and the I/A = nev equation given in the problem, to derive the equation v = IB/(ned) and then you will know exactly how these variables fit this problem.