Ascientist measuring the resistivity of a new metal alloy left her ammeter in another lab, but she does have a magnetic field probe. so she creates a 6.0-m-long, 4.0-mm-diameter wire of the material, connects it to a 1.5 v battery, and measures a 3.5 mt magnetic field 1.0 mm from the surface of the wire. what is the material’s resistivity?

Explanation:

The magnetic field produced by the wire is given by:

where

B = 3.5 mT = 0.0035 T is the magnetic field

is the vacuum permeability

is the current

r = 1.0 mm = 0.001 m is the distance from the wire

Solving for I, we find the current in the wire

Now we can find the resistance of the wire, R, by using Ohm's law:

And the resistance is related to the material's resistivity () by

where

L = 6.0 m is the length of the wire

is the cross-sectional area of the wire

Solving for , we find

the area between the graph and the t axis