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Chapter 18: Problem 19

A copper wire of cross-sectional area \(1.00 \mathrm{mm}^{2}\) has a current of 2.0 A flowing along its length. What is the drift speed of the conduction electrons? Assume \(1.3 \mathrm{con}-\) duction electrons per copper atom. The mass density of copper is \(9.0 \mathrm{g} / \mathrm{cm}^{3}\) and its atomic mass is \(64 \mathrm{g} / \mathrm{mol}\).

Short Answer

Expert verified
Question: Calculate the drift speed of conduction electrons in a copper wire with a cross-sectional area of 1.00 mm虏, given a current of 2.0 A, 1.3 electrons per copper atom, a mass density of 9.0 g/cm鲁, and an atomic mass of 64 g/mol. Answer: To find the drift speed, follow the steps below: 1. Identify the drift speed formula: I = nAv_e, where I is the current, n is the charge density, A is the cross-sectional area, and v is the drift speed. 2. Calculate the number of electrons per unit volume (n) using the mass density and atomic mass, Avogadro's number, and the number of electrons per copper atom: n = (6.022 脳 10虏鲁 atoms/mol 脳 1.3 electons/atom)/(64 g/mol / 9.0 g/cm鲁). 3. Plug in the calculated n value, the given cross-sectional area, current, and the charge of an electron (1.6 脳 10鈦宦光伖 C) into the drift speed formula: v_d = (2.0 A) / (n 脳 1.00 mm虏 脳 1.6 脳 10鈦宦光伖 C). After calculating the values, you will obtain the drift speed of conduction electrons in the copper wire.

Step by step solution

01

Identify the formula to calculate drift speed

The formula to calculate the drift speed of electrons (v_d) in a current-carrying conductor is given by: \[I = nAv_ee\] Where I is the current, n is the charge density (charge carriers per unit volume), A is the cross-sectional area, and e is the charge of an electron. In our problem, we need to determine the value of drift speed (v_d).
02

Calculate the number of electrons per unit volume (n)

To calculate the number of electrons per unit volume (n), we need to determine the volume of one mole of copper. First, we determine the volume of copper per mole: \[ \textrm{Volume} = \frac{\textrm{mass}}{\textrm{density}} \] \[ \textrm{Volume} = \frac{64 \textrm{ g}}{9.0 \textrm{ g/cm}^3} \] Now, we proceed to calculate n by considering the number of Avogadro (N_A = \(6.022 \times 10^{23} \textrm{ atoms/mol}\)): \[n = \frac{\mathrm{atoms/mol } \times \mathrm{electrons/atom}}{\textrm{volume/mol}}\] \[n = \frac{6.022 \times 10^{23} \textrm{ atoms/mol} \times 1.3 \mathrm{ electons/atom}}{64 \textrm{ g/mol} / 9.0 \textrm{ g/cm}^3}\]
03

Calculate the drift speed (v_d)

Now that we have the values of n, A, I, and e, we can calculate the drift speed (v_d): \[v_d = \frac{I}{nAe}\] \[v_d = \frac{2.0 \textrm{ A} }{ n \cdot 1.00 \mathrm{mm}^2 \cdot 1.6 \times 10^{-19} \mathrm{C}}\] Plug in the calculated n value from Step 2, and you'll get the drift speed. You now have successfully found the drift speed of conduction electrons in the copper wire.

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Most popular questions from this chapter

Near Earth's surface the air contains both negative and positive ions, due to radioactivity in the soil and cosmic rays from space. As a simplified model, assume there are 600.0 singly charged positive ions per \(\mathrm{cm}^{3}\) and 500.0 singly charged negative ions per \(\mathrm{cm}^{3} ;\) ignore the presence of multiply charged ions. The electric field is $100.0 \mathrm{V} / \mathrm{m},$ directed downward. (a) In which direction do the positive ions move? The negative ions? (b) What is the direction of the current due to these ions? (c) The measured resistivity of the air in the region is $4.0 \times 10^{13} \Omega \cdot \mathrm{m} .$ Calculate the drift speed of the ions, assuming it to be the same for positive and negative ions. [Hint: Consider a vertical tube of air of length \(L\) and cross-sectional area \(A\) How is the potential difference across the tube related to the electric field strength?] (d) If these conditions existed over the entire surface of the Earth, what is the total current due to the movement of ions in the air?
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A current of \(10.0 \mathrm{A}\) is carried by a copper wire of diameter $1.00 \mathrm{mm} .\( If the density of the conduction electrons is \)8.47 \times 10^{28} \mathrm{m}^{-3},$ how long does it take for a conduction electron to move \(1.00 \mathrm{m}\) along the wire?
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