Question

A particular conductor is x = 50.0 mm long by y = 10.0 mm wide by z = 1.0 mm thick.

This conductor is inserted into a 0.50 T magnetic field aligned parallel to the z-axis. When a 1.00 A current passes through the strip parallel to the x-axis, the Hall voltage is 100.0 µV.

What is the density of charge carriers in the conductor?

(1) 8.9 x 1024 m-3

(2) 3.1 x 1025 m-3

(3) 5.4 x 1025 m-3

(4) 7.2 x 1025 m-3

(5) 9.4 x 1025 m-3

Answer 1

Here we will use the fallowing relation as,

Hall Voltage =   =

Current through rod in the x-direction =

Charge carrier density

Width of the rod in z-axis ( axis parallel to magnetic field direction ) =

elementary charge =

Magnitude of magnetic field =

rearranging above equation we get charge carrier density   as,

Using the given values in above equation we get

The basic theory behind Classical Hall effect is that when charges move at some angle with respect to direction of magnetic field they experience force in the direction perpendicular to the plane containing the magnetic field vector and velocity vector.

The Force is on a charge   moving with velocity in magnetic field is given as,