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 scctional area of 4.99 cm2 across its width, a front to rear length of 19.6 cm, and a resistance of 1150 2. The block's material contains 4.67 x 1022 conduction electrons/m3. A potential difference of 45.1 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

Explanation / Answer

part a )

current = I = V/R

given V = 45.1 V

R = 1150 ohm

I = 45.1/1150 = 0.039 A

part b )

current density = J = I/A

given A = 4.99 cm^2 = 4.99 x 10^-4 m^2

J = 78.59 A/m^2

part c )

drift velocity = vd = J/ne

n = number of conduction electron = 4.67 x 10^22 electrons/m^3

e = 1.6 x 10^_19

vd = 0.0105 m/s = 1.05 x 10^-2 m/s

part d )

E = V/d = V/L

L = 19.6 cm = 0.196 m

E = 45.1/0.196 = 230 V/m

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