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Unformatted text preview: EE1 Spring 2008 Homework #6 Solutions (1) An infinitely long wire carrying a 25-A current in the positive x- direction is placed along the x-axis in the vicinity of a 20-turn circular loop located in the xy plane as shown in the following Figure. If the magnetic field at the center of the loop is zero, what is the direction and magnitude of the current flowing in the loop? To satisfy the condition that B = 0 at the center of the loop, the mag- netic flux from the infinitely long wire must cancel out the magnetic flux of the loop. For the infinitely long wire at the center of the loop: B 1 = μ I 1 2 πd ˆ z where ˆ z is coming out of the page. To cancel out the flux B 1 , it is clear that we must have the loop produce a flux B 2 that is in the opposite direction- ˆ z . By the right-hand rule, the current I 2 must travel clockwise in the loop. At the center of the loop: B 2 = μ NI 2 2 a ˆ- z where N is the number of turns and a is the radius of the loop. We can now equate the two flux densities and solve for the current...
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- Spring '08
- Magnetic Field, loop, infinitely long wire