Chapter 26, Problem 033 A block in the shape of a rectangular solid has a cross-

Question

Chapter 26, Problem 033 A block in the shape of a rectangular solid has a cross-sectional area of 4.25 cm2 across its width, a front-to-rear length of 15.9 cm, and a resistance of 897 . The block's material contains 6.72 × 1022 conduction electrons/m. A potential difference of 31.6 V is maintained between its front and rear faces. (a) what is the current in the block? (b) If the current density is uniform, what is its magnitude? What are (c) the drift velocity of the conduction electrons and (d) the magnitude of the electric field in the block? (a) Number (b) Number (c) Number (d) Number Units Units Units Units SHOW HINT LINK TO TEXT LINK TO SAMPLE PROBLEM LINK TO SAMPLE PROBLEM VIDEO MINI LECTURE VIDEO MINI-LECTURE Question Attempts: 0 of 5 used SAVE FOR LATER SUBMIT ANSWER

Explanation / Answer

Given Cross sectional area A = 4.25 cm2 = 4.25 x 10-4 m2

distance between top and bottom planes d = 15.9 cm = 15.9 x 10-2 m

Resistance R = 897 ohms

No. of conduction electrons per unit volume n = 6.72 x 1022

Voltage applied V = 31.6 V

a) current in the block I = V/R = 31.6/897 =0.035 A

b) current density J = I/A = 0.035 / 4.25 x 10-4 = 82.89 A/m2 = 83 A/m2

c) drift velocity Vd = J/n.e = 82.89 / (  6.72 x 1022 x1.6 x 10-19 )

= 7.709 x 10-3 m/s

d) Electric field E = V/d = 31.6/15.9 x 10-2 = 199 V/m

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