# _015 - Solution for Homework 15 Adding Magnetic Fields...

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Solution for Homework 15 Adding Magnetic Fields Solution to Homework Problem 15.1(The Magnetic Field Direction Due to Two Current- Carrying Wires at a Given Point) Problem: The fgure shows two current-carrying wires, one current pointing out oF the page and one pointing into the page. The wire carry currents oF equal magnitude. A point p is located halFway between the two wires. What is the direction oF the total magnetic feld at point p due to the two current-carrying wires? Select One oF the ±ollowing: (a-Answer) The magnetic feld points upward. (b) The magnetic feld points downward. (c) The magnetic feld points to the right. (d) The magnetic feld points to the leFt. p Solution (a) The magnetic feld due to the leFthand wire at point p can be Found using the right-hand rule to have a component upward and a component to the right. (b) The magnetic feld due to the righthand wire at point p can be Found using the right-hand rule to have a component upward and a component to the leFt. (c) Because point p is midway between the two current-carrying wires, the magnetic felds are equal in magnitude. Thus, the magnetic feld components to the right and leFt cancel. This leaves a magnetic feld with a component only upward. Total Points for Problem: 3 Points Solution to Homework Problem 15.2(Magnetic Field from Two Parallel Wires) Problem: Two infnite straight wires carrying current 2A in the y direction run parallel to the y -axis through the points ± 1cmˆx . Compute the magnetic feld at the point +2cmˆx . Select One oF the ±ollowing: (a) 9 × 10 2 z (b) 3 1 3 × 10 4 z (c) 7 2 3 × 10 5 z (d-Answer) 5 1 3 × 10 5 z (e) 0 Solution 1

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z x P I I y axis into page B 1P B 2P B P Defnitions v B 1 P Magnetic Field o± Wire 1 v B 2 P Magnetic Field o± Wire 2 v B P Total Magnetic Field at Point P Strategy: Compute the feld o± each individual wire and add the felds. (a) Draw the System and a Right-Handed Coordinate System: The current ²ows in the + y direction, so draw the system in the x z plane. For a right handed coordinate system, ˆ z = ˆ x × ˆ y , there±ore the positive y axis is into the page. (b) Compute B 1 P : The magnitude o± the magnetic feld ±rom wire 1 at the point P is given by the feld o± an infnite straight wire at a distance r 1 P = 3cm ±rom the wire, B 1 P = μ 0 I 2 πr 1 P = (4 π × 10 7 Tm A )(2A) 2 π (0 . 03m) = 4 3 × 10 5 T (c) Compute B 2 P : The magnitude o± the magnetic feld ±rom wire 2 at the point P is given by the feld o± an infnite straight wire at a distance r 2 P = 1cm ±rom the wire, B 2 P = μ 0 I 2 πr 2 P = (4 π × 10 7 Tm A )(2A) 2 π (0 . 01m) = 4 × 10 5 T (d) Find the Direction of the Fields: The magnetic feld lines ±rom each wire are circles concentric with the wire. Using the right hand rule ±or the wire and pointing the thumb o± the right hand into the page in the direction o± current, the feld is oriented clockwise. There±ore the feld o± each wire points in the negative z direction at point P .
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## This note was uploaded on 05/04/2008 for the course PHYS 2074 taught by Professor Stewart during the Winter '08 term at Arkansas.

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_015 - Solution for Homework 15 Adding Magnetic Fields...

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