1 2 3 4 5 6 7 Two infinite sheets of current flow parallel to the y-z plane as s
ID: 2305506 • Letter: 1
Question
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Two infinite sheets of current flow parallel to the y-z plane as shown. The sheets are equally spaced from the origin by xo = 7.9 cm. Each sheet consists of an infinite array of wires with a density n = 17 wires/cm. Each wire in the left sheet carries a current I1 = 2.9 A in the negative z-direction. Each wire in the right sheet carries a current I2= 3.7 A in the positive z-direction.
1)
What is Bx(P), the x-component of the magnetic field at point P, located at (x,y) = (-3.95 cm, 0)?T
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2)
What is By(P), the y-component of the magnetic field at point P, located at (x,y) = (-3.95 cm, 0)?T
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3)
What is By(R), the y-component of the magnetic field at point R, located at (x,y) = (-11.85 cm, 0)?T
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4)
What is
?B? ?dl? ?B??dl?
where the integral is taken around the dotted path shown, from a to b to c to d to a. The path is a trapazoid with sides ab and cd having length 9.5 cm, side ad having length 8.4 cm, and side bc having length 11.8 cm. The height of the trapezoid is H = 9.3 cm.T-m
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5)
What is By(S), the y-component of the magnetic field at point S, located at (x,y) = ( 11.85 cm, 0)?T
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6)
What is
?abB? ?dl? ?abB??dl?
where the integral is taken along the dotted line shown, from a to b.T-m
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(Survey Question)
7)
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Explanation / Answer
From Ampere's circuital law
B.dl - mu*I
B = mU.I/2L = mu/2*(I/L)
a) 0
b) B = (4*pi*10^-7) *1700(3.7 + 2.9)/2 = -0.0070 T
c) B = (4*pi*10^-7) *1700(-3.7 + 2.9)/2 = -0.00085 T
d) (-0.0070 + 0.00085 )*0.093 = -0.000572 T.m
e) B = (4*pi*10^-7) *1700(3.7-2.9)/2 = 0.00085 T
F) -0.0070*0.093 = -0.000651 T.M
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