The number density of conduction electrons in a particular metal is 1029 m-3. A current of 4 A flows through a wire of this material, which has a length of 1m and cross-sectional area of 2(mm)2. The voltage across the wire is 2.70x10-3 V. What is the average speed (drift speed) of the electrons in units of ms-1 to 3 significant figures using scientific notation (e.g. x.xxExx)?
Question
The number density of conduction electrons in a particular metal is 1029 m-3. A current of 4 A flows through a wire of this material, which has a length of 1m and cross-sectional area of 2(mm)2. The voltage across the wire is 2.70x10-3 V. What is the average speed (drift speed) of the electrons in units of ms-1 to 3 significant figures using scientific notation (e.g. x.xxExx)?
Solution
The drift speed (v) of the electrons can be calculated using the formula:
v = I / (n * A * e)
where: I is the current, n is the number density of conduction electrons, A is the cross-sectional area of the wire, and e is the elementary charge (1.6 x 10^-19 C).
First, we need to convert the given cross-sectional area to the correct units:
A = 2 mm^2 = 2 x 10^-6 m^2
Now we can substitute the given values into the formula:
v = 4 A / (10^29 m^-3 * 2 x 10^-6 m^2 * 1.6 x 10^-19 C) v = 1.25 x 10^-5 m/s
So, the average speed (drift speed) of the electrons is approximately 1.25 x 10^-5 m/s. To 3 significant figures in scientific notation, this is 1.25 x 10^-5 m/s.
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