A block in the shape of a rectangular solid has a cross-sectional area of 4.00 cm2 across its width, a front-to-rear length of 13.1 cm, and a resistance of 1190 Ω. The block's material contains 6.35 * 1022 conduction electrons/m3. A potential difference of 34.7 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?

Question

Physics

Brooke Ho

11 August, 19:31

A block in the shape of a rectangular solid has a cross-sectional area of 4.00 cm2 across its width, a front-to-rear length of 13.1 cm, and a resistance of 1190 Ω. The block's material contains 6.35 * 1022 conduction electrons/m3. A potential difference of 34.7 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?

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Hans · Answer 1

Area of crossection, A = 4 cm²

Length, l = 13.1 cm = 0.131 m

Resistance, R = 1190 ohm

conduction electron density, n = 6.35 x 10^22 / m³

Voltage, V = 34.7 V

(a) According to ohm's law

V = i x R

34.7 = i x 1190

i = 0.029 A

(b) Let the current density is J.

J = i / A

J = 0.029 / (4 x 10^-4)

J = 72.9 A/m²

(c) Let v is the drift velocity

By the use of the formula

i = n e A v

0.029 = 6.35 x 10^22 x 1.6 x 10^-19 x 4 x 10^-4 x v

0.029 = 4.064 v

v = 7.14 x 10^-3 m/s

(d) Let teh electric field is E

E = V l

E = 34.7 / 0.131

E = 264.9 V/m