Magnetic Field due to Current. April 22-26

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Edwin Berry
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1 Today Questions re: Magnetism problems 2 HW: Magnetism problems 2.5 NEW concept: Magnetic field produced by an Electric Current > Magnetic Field through a current loop > Magnetic Field inside a Solenoid Magnetic Force between 2 parallel wires

2 Magnetic Field produced by a Current through a straight wire: When a current I flows through a wire, there is a magnetic field B generated by that current, such that B = µ 0 I 2πR where µ 0 is called the "Permeability of Free Space", a constant whose defined value is 4π E-7 T*m/A, and R is the "perpendicular distance" from the wire. To find the direction of this magnetic field, we use a second Right Hand Rule: Point your thumb in the direction of the current through the wire; Curl your fingers "around the wire"; this circular direction is the direction of the magnetic field. A key idea here is that the magnetic field will completely circle around the wire; the magnetic field "turns" in the directions that your fingers "curl". Note: the magnetic field is always such that, if you look at the wire as the current comes TOWARDS YOU, the magnetic field will circle the wire counter-clockwise.

3 Examples: 1. A power wire carries a 10 A current to a microwave oven. What is the strength of the magnetic field produced by this current a distance of 0.10 m from the wire? 2. In a Physics lab, students powered small light bulbs with a 2.5 A current. If a detector were placed a distance of 0.40 m from the wire, what is the strength of the magnetic field due to this current? Note that the Earth's magnetic field has a magnitude of 5 E-5 T; how does the magnetic field due to the current compare to Earth's magnetic field? 3. For the following diagrams, where the arrow indicates the direction of the current, describe or draw the direction of the magnetic field.

4 Magnetic Field due to a Current in a wire loop: If a wire is formed into a loop, when current flows through the loop, a magnetic field will be set up such that the magnetic field will pass through the center of the loop. In the diagram to the left, the magnetic field produced moves through the loop from Left to Right; to determine the direction of the magnetic field through a loop, we have, yes, a third right-hand rule: Curl your fingers in the direction of the current through the loop; Your thumb will tell the direction of the magnetic field through the center of the loop. This was a very important discovery; it showed physicists that they could take a Circular magnetic field, where they could easily control its strength by increasing or decreasing the current, and they could make that circular field point in a specific direction (through the center of the loop).

5 Magnetic Field inside of a "Solenoid": A Solenoid is formed when a long straight wire is formed into a series of loops, or a coil. N S In the diagram to the left, the coil of wires carries a current I as shown. Each individual loop produces a magnetic field, and these are in the same direction (through the loops). These individual fields add together, giving us an overall magnetic field that passes through the solenoid. To determine the direction of the magnetic field through a solenoid, you can "wrap" or "curl" the fingers of your right hand in the direction that the current flows through the coil, and your thumb will point in the direction of B. To determine the strength (or magnitude) of the magnetic field inside the solenoid, we use the following expression: B = µ 0 IN = µ 0 In where µ 0 = 4π E-7, N represents the "number of loops" in the coil, L represents the "length" of the Solenoid itself, and n is referred to as the "loop density", or the "number of loops per unit length". [E.g., if a Solenoid is constructed with N = 50 loops, and the length of the solenoid is L = 0.10 m, then n = 50/0.10 = 500 loops per meter.] L

6 Solenoid as Electromagnet: We describe a Solenoid as an "Electromagnet"; literally, a device that uses Electricity to produce or create Magnetism. By running a current through the coil, we have a magnetic field that passes through the center of the coil. The diagram to the left compares an "Air Core" solenoid to an "Iron Core" solenoid. Of note is that, by filling the empty solenoid with an iron core, the magnetic field strength is increased (this is shown in the diagram with magnetic field lines that are greater in both number and density). Also, notice in the equation for B that the Iron Core introduces a constant k (this is referred to as the Relative Permeability); this is meant to imply that the field strength will increase by some number that is associated with iron (for Iron, k = 200). In essence, by filling the space with a magnetic material, you effectively increase the strength of the Electromagnet.

7 Force between 2 parallel wires: When two wires, 1 and 2, carrying currents I 1 and I 2, are oriented parallel to one another, separated by a distance d, they will exert a mutual force on one another such that we calculate the Force per unit Length F B = µ 0 I 1 I 2 L 2πd This force will either cause the wires to attract or repel each other. d I 1 In this configuration, where both wires carry currents in the same direction, the force will be attractive. When the currents are opposite, the force is repulsive. I 2 This seemingly inconsequential concept is actually of vital importance in Electricity; the definition of the unit of current (Ampere) is based on the force between two parallel wires: When two parallel wires are separated by a distance d = 1 m, there will be a mutually attractice force F = 2 E-7 N when the wires carry a current of 1 Ampere.

Chapter 30 - Magnetic Fields and Torque. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 30 - Magnetic Fields and Torque A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007 Objectives: After completing this module, you should