A block in the shape of a rectangular solid has a cross-sectional area of 2.98 c

Question

A block in the shape of a rectangular solid has a cross-sectional area of 2.98 cm2 across its width, a front-to-rear length of 22.6 cm, and a resistance of 1200 . The block's material contains 5.27 × 1022 conduction electrons/m3. A potential difference of 32.4 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?

Explanation / Answer

Given,

A = 2.98 cm^2 ; L = 22.6 cm ; R = 1200 Ohm

n = 5.27 x 10^22 e/m^2 ; V = 32.4 V ;

a)We know from Ohm's law

V = IR => I = V/R = 32.4/1200 = 0.027 A

Hence, I = 0.027 A

b)We know that

J = I/A = 0.027/2.98 x 10^-4 = 90.6 A/m^2

Hence, J = 90.6 A/m^2

c)We know that

J = n e Vd

Vd = J/n e

Vd = 90.6/(5.27 x 10^22 x 1.6 x 10^-19) = 1.1 x 10^-2 m/s

Hence, Vd = 1.1 x 10^-2 m/s

d)E = V/d

E = 32.4/0.226 = 143.36 V/m

Hence, E = 143.36 V/m

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