Question:
A current of 5 A passes through a copper conductor (resistivity = \(1.7\times10^{-8}\ \Omega\,\mathrm{m}\)) of radius of cross-section 5 mm. Find the mobility of the charges if their drift velocity is \(1.1\times10^{-3}\) m/s.
A current of 5 A passes through a copper conductor (resistivity = \(1.7\times10^{-8}\ \Omega\,\mathrm{m}\)) of radius of cross-section 5 mm. Find the mobility of the charges if their drift velocity is \(1.1\times10^{-3}\) m/s.
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Mobility \(\mu=v_d/E\) and the field in the conductor is \(E=\rho J=\rho I/A\).
Updated On: Nov 5, 2026
- \(1.3\ \mathrm{m^2/Vs}\)
- \(1.0\ \mathrm{m^2/Vs}\)
- \(1.8\ \mathrm{m^2/Vs}\)
- \(1.5\ \mathrm{m^2/Vs}\)
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The Correct Option is B
Solution and Explanation
Area: \(A=\pi r^2=\pi(5\times10^{-3})^2=7.85\times10^{-5}\ \mathrm{m^2}\).
Current density: \(J=\dfrac{I}{A}=\dfrac{5}{7.85\times10^{-5}}=6.37\times10^{4}\ \mathrm{A/m^2}\).
Electric field: \(E=\rho J=1.7\times10^{-8}\times6.37\times10^{4}=1.08\times10^{-3}\ \mathrm{V/m}\).
Mobility: \(\mu=\dfrac{v_d}{E}=\dfrac{1.1\times10^{-3}}{1.08\times10^{-3}}\approx1.0\ \mathrm{m^2/Vs}\).
Answer: (2) 1.0 m2/Vs
Current density: \(J=\dfrac{I}{A}=\dfrac{5}{7.85\times10^{-5}}=6.37\times10^{4}\ \mathrm{A/m^2}\).
Electric field: \(E=\rho J=1.7\times10^{-8}\times6.37\times10^{4}=1.08\times10^{-3}\ \mathrm{V/m}\).
Mobility: \(\mu=\dfrac{v_d}{E}=\dfrac{1.1\times10^{-3}}{1.08\times10^{-3}}\approx1.0\ \mathrm{m^2/Vs}\).
Answer: (2) 1.0 m2/Vs
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