The cross section of a copper strip is 1.00 mm think and 20 mmwide. There is a 1

Question

The cross section of a copper strip is 1.00 mm think and 20 mmwide. There is a 10 A current through this cross section, with the charge carrier traveling down the length of the strip. The strip is placed in a uniform magnetic feild that has a magnitude of 2 T and is directed perpendicular to both the length and the width of the strip. If the number density of free electrons in copper is 8.47 x 10^19 mm^-3, calculate a.) the speed of the electrons in the strip and b.) the potential difference across the strip width.

Answers:

a) 3.7x10

Explanation / Answer

Given that,

thickness = t = 1.00 mm = 0.001 m

width = w = 20mm = 0.02 m

current in the strip = i =10 A

Magebtic field = B = 2 T

n = 8.47 x 1019 mm3 = 8.47 x 1019 x 10-9 m3 = 8.47 x 1010 m3

lets first solve part (b) Let V be the potential diff.

we know that

n = i B / e t V, from this we get, (where e is the charge on e-)

V = i B / e t n

V = 10 x 2 / 1.6 x 10-19 x 8.47 x 1010 x 0.001 = 1.475 x 106 V

Hence V = 1.5 x 106 V

(a) let v be the speed. We have the relation,

v = V / w B = 1.5 x 106 V / 0.02 x 2 = 37.5 x 106 m/s = 3.75 x 105 m/s

Hence, speed = v = 3.75 x 105 m/s

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