Task 1- Faraday's law As illustrated in Figure I, a rectangular wire loop carries current i, has height a, width a, and is centered on the origin. It can rotate about the : axis. For rotation angle d, the surface normal of the rectangle enclosed by the loop is i = i cos o+ ý sin d, and the vectors representing the four sides of the loop are k= -aj coso + ai sin o h = -h I = -l The magnetic flux density is à Bo everywhere. (a) What is the magnetic flux through the loop as a function of o?
Task 1- Faraday's law As illustrated in Figure I, a rectangular wire loop carries current i, has height a, width a, and is centered on the origin. It can rotate about the : axis. For rotation angle d, the surface normal of the rectangle enclosed by the loop is i = i cos o+ ý sin d, and the vectors representing the four sides of the loop are k= -aj coso + ai sin o h = -h I = -l The magnetic flux density is à Bo everywhere. (a) What is the magnetic flux through the loop as a function of o?
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![Task 1- Faraday's law
As illustrated in Figure 1, a rectangular wire loop carries current i, has height b, width a, and is
centered on the origin. It can rotate about the z axis. For rotation angle d, the surface normal of
the rectangle enclosed by the loop is i = i cos 6 + ý sin d, and the vectors representing the four
sides of the loop are
l2 = -aý cos o + aử sin ở
l = -l
1 = -
The magnetic flux density is & By everywhere.
(a) What is the magnetic flux through the loop as a function of 6?
12 =
-aý cos o
+at sin o
13 =
-l
B-B
1 =
-1
+ ý sin o
Figure 1: Geometry of wire loop rotating in magnetic field.
Project 2 Worksheet Solutions
(b) Assuming o = wt, what is the voltage induced in the loop as a function of o?
v(t) :](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5312a15-860e-407c-ae9e-8729c86c8316%2F496aaffa-83ce-4a52-a727-a391f50875f8%2Fledxnie_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Task 1- Faraday's law
As illustrated in Figure 1, a rectangular wire loop carries current i, has height b, width a, and is
centered on the origin. It can rotate about the z axis. For rotation angle d, the surface normal of
the rectangle enclosed by the loop is i = i cos 6 + ý sin d, and the vectors representing the four
sides of the loop are
l2 = -aý cos o + aử sin ở
l = -l
1 = -
The magnetic flux density is & By everywhere.
(a) What is the magnetic flux through the loop as a function of 6?
12 =
-aý cos o
+at sin o
13 =
-l
B-B
1 =
-1
+ ý sin o
Figure 1: Geometry of wire loop rotating in magnetic field.
Project 2 Worksheet Solutions
(b) Assuming o = wt, what is the voltage induced in the loop as a function of o?
v(t) :
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