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)
(Charge on electron = 1.6 × 10–19C)
Correct Answer: 136
Approach Solution - 1
To determine the force experienced by a moving electron in a copper wire, we use the formula for current density \( J \) and electric field \( E \) in a conductor. The force \( F \) due to an electric field on a charge is \( F = eE \), where \( e = 1.6 \times 10^{-19} \) C is the charge of an electron.
Step 1: Calculate the Current Density
The current density \( J \) is defined as \( J = \frac{I}{A} \), where \( I = 1 \) A is the current and \( A = 2.0 \) mm2 is the cross-sectional area of the wire. Convert the area from mm2 to m2:
\( A = 2.0 \, \text{mm}^2 = 2.0 \times 10^{-6} \, \text{m}^2 \).
Thus, \( J = \frac{1}{2.0 \times 10^{-6}} = 5.0 \times 10^5 \, \text{A/m}^2 \).
Step 2: Calculate the Electric Field
Ohm's Law for conductors in terms of current density is \( J = \sigma E \), where \( \sigma = \frac{1}{\rho} \) is the conductivity and \( \rho = 1.7 \times 10^{-8} \, \Omega \, \text{m} \) is the resistivity. Thus,
\( E = J \rho = 5.0 \times 10^5 \times 1.7 \times 10^{-8} = 8.5 \times 10^{-3} \, \text{V/m} \).
Step 3: Calculate the Force on an Electron
The force \( F = eE = 1.6 \times 10^{-19} \times 8.5 \times 10^{-3} = 1.36 \times 10^{-21} \, \text{N} \).
Express the force in the desired format \( F = 1.36 \times 10^{-23} \times 10^2 = 136 \times 10^{-23} \, \text{N} \).
The computed value, \( 136 \), falls within the given range of 136,136. Thus, the force experienced by the electron is within the expected range.
Approach Solution -2
I = nevdA
\(J=\frac{E}{ρ}\)
\(F=eE=\frac{1.7×1.6×10^{−19}×10^{−8}}{2×10^{−6}}\)
\(=136×10^{–23}N\)
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Concepts Used:
Electric Current
Defining Electric Current
It is the rate of flow of electrons in a conductor. SI Unit - Ampere (A).
Electrons are negatively charged particles hence when they move a number of charges moves.
Note:- The ability of a particular substance to conduct electricity depends on the number of electrons that are able to move . Some of the materials allow current to flow better than others.
What is an Electromotive Force?
If a force acts on electrons to make them move in a particular direction, then up to some extent random motion of the electrons will be eliminated. An overall movement in one direction. The force which acts on the electrons to move them in a certain direction is known as electromotive force and its quantity is known as voltage and is measured in V.