Question

A 1 m long copper wire carries a current of 1 A. If the cross section of the wire is 2.0 mm² and the resistivity of copper is 1.7 × 10^–8 Ω, the force experienced by moving electron in the wire is ___ × 10^–23N.
(Charge on electron = 1.6 × 10^–19C)

Answer 1

Correct Answer: 136

To determine the force experienced by a moving electron in the wire, we need to find the electric field (E) within the wire. Using Ohm's law and properties of current, we can derive E as follows: 
We know resistivity \( \rho \), length \( L \), cross-sectional area \( A \), and the current \( I \) through the wire.
Step 1: Calculate the resistance (R) of the wire:
\[ R = \frac{\rho \cdot L}{A} \]
Where:
\( \rho = 1.7 \times 10^{-8} \, \Omega \cdot m \)
\( L = 1 \, m \)
\( A = 2.0 \, mm^2 = 2.0 \times 10^{-6} \, m^2 \)
Substituting these values gives:
\[ R = \frac{1.7 \times 10^{-8} \cdot 1}{2.0 \times 10^{-6}} = 8.5 \times 10^{-3} \, \Omega \]
Step 2: Calculate the electric field (E) in the wire:
\[ E = \frac{V}{L} \] where \( V = I \cdot R \)
Substitute \( I = 1 \, A \) and \( R = 8.5 \times 10^{-3} \, \Omega \) into the equation:
\[ V = 1 \times 8.5 \times 10^{-3} = 8.5 \times 10^{-3} \, V \]
\[ E = \frac{8.5 \times 10^{-3}}{1} = 8.5 \times 10^{-3} \, V/m \]
Step 3: Calculate the force (F) experienced by the electron:
\[ F = e \cdot E \] where \( e = 1.6 \times 10^{-19} \, C \)
\[ F = 1.6 \times 10^{-19} \times 8.5 \times 10^{-3} = 1.36 \times 10^{-21} \, N \]
Converting to required format:
\( F = 136 \times 10^{-23} \, N \)
This value \( (136) \) falls within the expected range 136,136.