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A varying current i(t) = t(10-t) A (t in seconds) flows through a long straight wire that lies along the x-axis. The current produces a magnetic field B whose magnitude at a distance r from the wire is B = HT. Furthermore, at the point P, B points away from the observer as shown in the figure.

A varying current i(t) = t(10-t) A (t in seconds) flows through a long straight wire that lies along the x-axis. The current produces a magnetic field B whose magnitude at a distance r from the wire is B = HT. Furthermore, at the point P, B points away from the observer as shown in the figure.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A varying current i(t) = t(10-t) A (t in seconds) flows through a long straight wire that lies along the x-axis. The current produces a magnetic field B whose magnitude at a distance r from the wire is B = T. Furthermore, at the point P, B points away from the observer as shown in the figure. Mol 2πr Wire loop C Rectangular region R Volt meter Φ(t) : = [E.. x=0 E. dr = B Calculate the flux (1), at time t, of B through a rectangle of dimensions L x H = 7 x 2 m whose top and bottom edges are parallel to the wire and whose bottom edge is located d = 0.5 m above the wire. Assume that the rectangle and the wire are located in the same plane. (Use symbolic notation and fractions where needed. Let I = i(t) and express your answer in terms of μo and I.) • P = (x, y) y H x=L Use Faraday's Law to determine the voltage drop around the rectangular loop (the boundary of the rectangle) at time t = 3. Assume Ho = 4T 10-7 T. m/A. (Use symbolic notation and fractions where needed.) T.m² V
Transcribed Image Text:A varying current i(t) = t(10-t) A (t in seconds) flows through a long straight wire that lies along the x-axis. The current produces a magnetic field B whose magnitude at a distance r from the wire is B = T. Furthermore, at the point P, B points away from the observer as shown in the figure. Mol 2πr Wire loop C Rectangular region R Volt meter Φ(t) : = [E.. x=0 E. dr = B Calculate the flux (1), at time t, of B through a rectangle of dimensions L x H = 7 x 2 m whose top and bottom edges are parallel to the wire and whose bottom edge is located d = 0.5 m above the wire. Assume that the rectangle and the wire are located in the same plane. (Use symbolic notation and fractions where needed. Let I = i(t) and express your answer in terms of μo and I.) • P = (x, y) y H x=L Use Faraday's Law to determine the voltage drop around the rectangular loop (the boundary of the rectangle) at time t = 3. Assume Ho = 4T 10-7 T. m/A. (Use symbolic notation and fractions where needed.) T.m² V
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