329sp10hw6sol - ECE 329 Spring 2010 Homework 6 Solution Due...

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Unformatted text preview: ECE 329 Spring 2010 Homework 6 - Solution Due: Mar. 2, 2010 1. The magnetic eld at the origin is a superposition of those generated by the two sheets. a) Since the currents are owing in z direction and they extend to in nity in both x and z directions, the magnetic eld is in the x direction. The magnetic elds generated by the sheet y = 1 and y =- 1 are H 1 = 1 μ μ · 2 2 ˆ x = ˆ x ( A/m ) , H 2 = 1 μ- μ · 2 2 ˆ x =- ˆ x ( A/m ) , respectively. Therefore, the total eld at the origin is H = H 1 + H 2 = ( A/m ) . b) Similar to a), we have H = H 1 + H 2 = 1 μ μ · 2 2 ˆ x + 1 μ- μ · (- 2) 2 ˆ x = 2ˆ x ( A/m ) . c) H = H 1 + H 2 = 1 μ- μ · 2 2 ˆ y + 1 μ- μ · 4 2 ˆ x + 1 μ μ · 2 2 ˆ y + 1 μ μ · 4 2 ˆ x = ( A/m ) . Note: Actually, we can directly obtain the results for a) and c) by using symmetry. 2. a) Biot-Savart law tells us that the direction of the magnetic eld generated by an in nitesimal current element is parallel to the cross product between the direction of the current and the vector joining the current element and the point under consideration. In our case, the current is parallel to ˆ y , then, using the right hand rule governing cross products, we can easily verify that in the region of z > along the ˆ z axis, B should be parallel to ˆ x : B || 2ˆ y × ˆ z →...
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This note was uploaded on 04/20/2010 for the course ECE ECE 329 taught by Professor Goddart during the Spring '10 term at University of Illinois at Urbana–Champaign.

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329sp10hw6sol - ECE 329 Spring 2010 Homework 6 Solution Due...

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