a) Calculate the y component of the magnetic field at the center of the square.
ID: 1261878 • Letter: A
Question
a) Calculate the y component of the magnetic field at the center of the square.
b) Calculate the x-component of the force on a 1.0-cm long piece of the lower right-hand wire, due to the other three wires.
The four wires that lie at the corners of a square of side a= 3.20 cm are carrying equal currents i= 1.10 A into (+) or out of (-) the page, as shown in the picture. The four wires that lie at the corners of a square of side a= 3.20 cm are carrying equal currents i= 1.10 A into (+) or out of (-) the page, as shown in the picture. a) Calculate the y component of the magnetic field at the center of the square. b) Calculate the x-component of the force on a 1.0-cm long piece of the lower right-hand wire, due to the other three wires.Explanation / Answer
The lower left wire pushes the lower right wire to the right.
F = uIIL/2pir
F = (4pi X 10-7)(1.1)2(.01)/2pi(.032)
F = 7.56 X 10-8 N
The diagonal wire will push down and to the right. The distance is from the Pythagorean Theorem
d2 = (.032)2 + (.032)2
d = .0453 m
F = (4pi X 10-7)(1.1)2(.01)/2pi(.0453)
F = 5.35 X 10-8 N
The x and y components are the same - multiply by cos45 to find them
Fx = 3.78 X 10-8 N
The net x = 3.78 X 10-8 + 7.56 X 10-8 = 1.134 X 10-7 N to the right
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