Question

A rectangular copper strip measures 1.0 mm in the direction of a uniform 2.8T magnetic field. When the strip carries a 7.2A current at right angles to the field, the Hall potential across the strip is 1.2uV .

Find the number density of free electrons in the copper.

Answer 1

To find the number density of free electrons in the copper strip using the Hall effect, we calculate it to be approximately 8.75 x 10^28 electrons per cubic meter.

Step-by-step explanation:

To find the number density of free electrons in the copper strip, we must use the Hall effect equation for Hall voltage (VH), which is given by:

VH = (B * I) / (n * e * t)

Where:

• B is the magnetic field (2.8T)
• I is the current (7.2A)
• n is the number density of electrons (unknown)
• e is the elementary charge (~1.602 x 10-19 Coulombs)
• t is the thickness of the copper strip (1.0 mm = 1.0 x 10-3 meters)
• VH is the Hall voltage (1.2µV = 1.2 x 10-6 Volts)

Rearranging the equation to solve for the number density (n), we get:

n = (B * I) / (e * t * VH)

Substituting the given values:

n = (2.8 * 7.2) / (1.602 x 10-19 * 1.0 x 10-3 * 1.2 x 10-6)

After calculating:

n ≈ 8.75 x 1028 electrons per cubic meter

This is the number density of free electrons in the copper strip.