Relation between Current and Drift Velocity - NEET Physics Questions
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Relation between Current and Drift Velocity

Practice Questions:
Question 21: easy

A copper wire of length \(1\text{ m}\) and radius \(\left(\frac{10^{-3}}{\sqrt{\pi}}\right)\text{ m}\) has electrical resistance of \(10\ \Omega\). The current density in the wire for an electric field strength of \(10\text{ V/m}\) is

1. \(10^5\text{ A/m}^2\)
2. \(10^6\text{ A/m}^2\)
3. \(2 \times 10^5\text{ A/m}^2\)
4. \(2 \times 10^6\text{ A/m}^2\)
View Answer

Area \(A = \pi r^2 = 10^{-6}\text{ m}^2\). Resistivity \(\rho = RA/l = 10 \times 10^{-6} / 1 = 10^{-5}\ \Omega\cdot\text{m}\). Conductivity \(\sigma = 1/\rho = 10^5\text{ S/m}\). Current density is \(J = \sigma E = 10^5 \times 10 = 10^6\text{ A/m}^2\).

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Question 22: moderate

Estimate the average drift speed of conduction electrons in a conductor of cross-sectional area \(10^{-7}\text{ m}^2\) carrying current of \(1.5\text{ A}\). The number density of conduction electrons is \(8.5 \times 10^{28}\text{ m}^{-3}\).

1. \(2.2\text{ mm s}^{-1}\)
2. \(1.1\text{ mm s}^{-1}\)
3. \(3.3\text{ mm s}^{-1}\)
4. \(0.1\text{ mm s}^{-1}\)
View Answer

Using the formula for drift velocity \(v_d = \frac{I}{n e A}\), we substitute the given values: \(v_d = \frac{1.5}{8.5 \times 10^{28} \times 1.6 \times 10^{-19} \times 10^{-7}} \approx 1.1 \times 10^{-3}\text{ m/s} = 1.1\text{ mm s}^{-1}\).

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