Embibe Experts Solutions for Exercise 2: EXERCISE

(a) A group of charges, each with charge $e$, moves with velocity $\overrightarrow{v}$. The number of particles per unit volume is $n$. What is the current density of these charges, in magnitude and direction? Make sure that your answer has units of $\mathrm{A} {\mathrm{m}}^{-2}$.

(b) We want to calculate how long it takes for an electron to get from a car battery to the starter motor after the ignition switch is turned. Assume that the current flowing is $115 \mathrm{A}$, and that the electrons travel through copper wire with cross-sectional area $31.2{ \mathrm{mm}}^2$ and length $85.5 \mathrm{cm}$. What is the current density in the wire? The number density of the conduction electrons in copper is $8.49\times {10}^{28} {\mathrm{m}}^{-3}$. Given this number density and the current density, what is the drift speed of the electrons? How long does it take for an electron starting at the battery to reach the starter motor? Assume no collision.

At what temperature, the resistance of a copper wire will become three times its value at $0°\mathrm{C}$ ? (The average temperature coefficient of resistance for copper $=4\times {10}^{-3}$ per ${}^{\circ }\mathrm{C}$ )?

A $5.80 \mathrm{m}$ length of $2.0 \mathrm{mm}$ diameter wire carries a $750 \mathrm{mA}$ current when $22.0\mathrm{mV}$ is applied to its ends. If the drift speed is $1.7\times {10}^{-5} {\mathrm{ms}}^{-1}$, determine

(a) The resistance $R$ of the wire

(b) The resistivity $\rho$, and

(c) The number $n$ of free electrons per unit volume.

At a point high in the Earth's atmosphere, ${\mathrm{He}}^{2+}$ ions in a concentration of $2.8\times {10}^{12} {\mathrm{m}}^{-3}$ are moving due north at a speed of $2.0\times {10}^6 \mathrm{m} {\mathrm{s}}^{-1}$. Also, a $7.0\times {10}^{11} {\mathrm{m}}^{-3}$ concentration of ${\mathrm{O}}_2^{-}$ions is moving due south at a speed of $7.2\times {10}^6 \mathrm{m} {\mathrm{s}}^{-1}$. Determine the magnitude and direction of the net current passing through unit area $\left(\mathrm{A} {\mathrm{m}}^{-2}\right)$.

An electrical conductor designed to carry large currents has a circular cross - section $2.50 \mathrm{mm}$ in diameter and is $14.0 \mathrm{m}$ long. The resistance between its ends is $0.104\mathrm{\Omega }$.

$\left(a \right)$ What is the resistivity of the material?

 $\left(b\right)$ If the electric field magnitude in the conductor is $1.28 \mathrm{V} {\mathrm{m}}^{-1}$, what is the total current?

 $\left(c\right)$ If the material has $8.5\times {10}^{28}$ free electrons per cubic metre, find the average drift speed under the conditions of part $\left(b\right)$.