_014 - Solution for Homework 15 Adding Magnetic Fields...

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Unformatted text preview: Solution for Homework 15 Adding Magnetic Fields Solution to Homework Problem 15.1(Magnetic Field from Two Parallel Wires) Problem: Two infinite straight wires carrying current 2A in the + y direction run parallel to the y-axis through the points 1cmx . Compute the magnetic field at the point +2cmx . Select One of the Following: (a) 9 10- 2 T z (b) 3 1 3 10- 4 T z (c) 7 2 3 10- 5 T z (d-Answer) 5 1 3 10- 5 T z (e) Solution z x P I I y axis into page B 1P B 2P B P Definitions vector B 1 P Magnetic Field of Wire 1 vector B 2 P Magnetic Field of Wire 2 vector B P Total Magnetic Field at Point P Strategy: Compute the field of each individual wire and add the fields. (a) Draw the System and a Right-Handed Coordinate System: The current flows in the + y direction, so draw the system in the x z plane. For a right handed coordinate system, z = x y , therefore the positive y axis is into the page. (b) Compute B 1 P : The magnitude of the magnetic field from wire 1 at the point P is given by the field of an infinite straight wire at a distance r 1 P = 3cm from the wire, B 1 P = I 2 r 1 P = (4 10- 7 Tm A )(2A) 2 (0 . 03m) = 4 3 10- 5 T (c) Compute B 2 P : The magnitude of the magnetic field from wire 2 at the point P is given by the field of an infinite straight wire at a distance r 2 P = 1cm from the wire, B 2 P = I 2 r 2 P = (4 10- 7 Tm A )(2A) 2 (0 . 01m) = 4 10- 5 T (d) Find the Direction of the Fields: The magnetic field lines from each wire are circles concentric with the wire. Using the right hand rule for the wire and pointing the thumb of the right hand into the page in the direction 1 of current, the field is oriented clockwise. Therefore the field of each wire points in the negative z direction at point P . vector B 1 P = 4 3 10- 5 T z vector B 2 P = 4 10- 5 T z (e) Compute the Total Field: By linear superposition, the total magnetic field at the point P is vector B P = vector B 1 P + vector B 2 P = 4 3 10- 5 T z 4 10- 5 T z = 5 1 3 10- 5 T z Total Points for Problem: 3 Points Solution to Homework Problem 15.2(Magnetic Field of Segment of Loop) Problem: A segment of a circular loop of wire lies in the y z plane. It occupies the 1 4 plane with y > and z > , so the loop forms one quarter of a circle. The wire carries a current I . Compute the magnetic field at the origin. Select One of the Following: (a) I 2 R x (b) I 2 R x (c) I 8 R x (d-Answer) I 8 R x (e) y z I R Solution y z I x out of page B in to page at origin R Definitions vector B Magnetic Field at Origin I Current in Loop R Radius of Loop vector Vector in direction of current 2 Strategy: Integrate the Biot-Savart Law over the segment of the loop....
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This note was uploaded on 05/04/2008 for the course PHYS 2074 taught by Professor Stewart during the Spring '08 term at Arkansas.

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_014 - Solution for Homework 15 Adding Magnetic Fields...

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