Final answer:
To find the number density of free electrons in the copper strip using the Hall effect, the Hall voltage formula is used, and the given values are substituted into the rearranged equation. After calculation, the number density in electrons per cubic meter is obtained.
Step-by-step explanation:
The student's question pertains to the concept of the Hall effect in physics, more specifically, the determination of the number density of free electrons in copper due to a given Hall potential. The Hall effect is the production of a potential difference (the Hall potential) across an electrical conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current. According to the Hall effect formula, the Hall voltage (VH) is given by:
To find the number density of free electrons (n), we rearrange the formula
We are given:
- Current (I) = 7.3 A
- Magnetic field (B) = 2.9 T
- Hall potential (VH) = 1.2 µV = 1.2 x 10-6 V
- Thickness of the strip = 1.0 mm = 1.0 x 10-3 m (assuming the width of the strip is very large compared to its thickness)
Since the current is perpendicular to the magnetic field, and the area A is simply the cross-section through which the current flows, A = thickness x width. We assume a large width, which allows us to not include it in our calculation:
A = 1.0 x 10-3 m2
The known value of the elementary charge e is approximately 1.602 x 10-19 Coulombs. Substituting all values into our formula, we get:
n = rac{7.3 A × 2.9 T}{(1.602 x 10-19 C) × (1.0 x 10-3 m2) × (1.2 x 10-6 V)}
Upon calculation, you can find the number density n of free electrons in the copper strip. The units of n will be electrons per cubic meter (electrons/m3).