Main Answer
When a conductor of cross-sectional area 5 x 10⁻⁶ m² carries a current of 6 A, the drift velocity of the conduction electrons is 1.2 x 10⁻⁴ m/s. The number density (number per unit volume) of the conduction electrons is 3.0 x 10²⁴ electrons/m³.The correct answer is 3.0 x 10²⁴ electrons/m³ option B.
Step-by-step explanation
To find the number density of the conduction electrons, we first need to calculate the total number of electrons in the conductor. The number of electrons is given by the charge carried by the current (6 C) divided by the charge on each electron (-1.6 x 10⁻¹⁹ C):number of electrons = charge / charge per electron= (6 C) / (-1.6 x 10⁻¹⁹ C) = 3.75 x 10²⁰ electrons.
Next, we need to find the volume of the conductor. The volume is given by the cross-sectional area and the length of the conductor:
volume = cross-sectional area length
= (5 x 10⁻⁶ m²) (length in meters).
Now, we can divide the total number of electrons by the volume to get the number density:
number density = total number of electrons / volume
= (3.75 x 10²⁰ electrons) / (length in meters) (5 x 10⁻⁶ m²)
= 3.0 x 10²⁴ electrons/m³.
The correct answer is 3.0 x 10²⁴ electrons/m³ option B.