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Magnetic Fields and Forces Notes Sheet 1. Magnetic fields from a bar magnet The picture top left shows the familiar pattern of magnetic fields from a permanent bar magnet. 2. Magnetic fields from Long Straight Wire: The magnetic field direction around a long straight wire is given by a right hand rule as shown by the image top right. Notice that the fields circle around the wire and get weaker at distances farther from the wire. The equation B= μo I 2πr where B is the magnetic field in units of Tesla, µo = 1.26 x 10-6 T·m/A , I is current in Amps, and r is the distance outward from the wire in units of meters. 3. Magnetic fields from a long solenoid : The magnetic field is concentrated into a nearly uniform field at the center of the coil. The field outside is weaker and loops back as shown. The direction of the field in the center is given by another right hand rule where the fingers of the right hand are curled in the direction of the current in the coils and the thumb points in the direction of the magnetic field within the solenoid. The equation for the magnetic field in the interior of the solenoid is given by the equation B = μo n I where n is the number of turns per unit length and I is the current through the coil. Magnetic fields from a more loosely wrapped coil might be represented by the image at the right. 4. Force from charges moving through a magnetic field: The diagram at the right gives two versions of the right hand rule for determining the direction of the force on a charged particle moving through a magnetic field. It should be emphasized that The force is perpendicular to both the velocity v of the charge q and the magnetic field B. The magnitude of the force is maximized when the direction of the velocity and the magnetic field are perpendicular to each other. The magnitude of the force for more general circumstances is given by the equation F = qvB sinθ where θ is the angle between the velocity and the magnetic field, q is the charge on the moving particle, v is the velocity, and B is the magnetic field. This equation correctly states that the magnetic force on a stationary charge or a charge moving parallel to the magnetic field is zero. The force for the preferred orientation of magnetic field and velocity being perpendicular to each other is given by the equation F=qvB 5. Force on a wire carrying current in a magnetic field Since a wire carrying current is equivalent to charges moving through the wire, there is a magnetic force on these moving charges as well. In this discussion we consider conventional (not electron) current flow. The equation for the force on a wire of length L in a magnetic field B is F=ILB It should be clear that it is not the total length of a wire that goes into the equation above but rather the portion in the magnetic field. The diagram to the right shows the similarity between charges moving through a wire and in a vacuum. 6. Memory aid for force equations: Since the charge on an electron is given the symbol e, having a value of 1.6 x 10-19 Coulomb, students have used the following memory aid to help remember the two equations above. In the memory aid, the equations the force is equal to the sweethearts Bev and Bil. Maybe it helps. F = Bev & F = Bil 7. Force between two wires carrying current: There are many examples of a wire carrying current in the neighborhood of other current carrying wires and interacting through the mechanism of magnetic fields. The simplest example is two long straight wires separated by a distance. In this example we are interested only in the direction of the forces and will not give the force equation. If we consider wire 1 carrying current I1 producing a magnetic field at the location of wire 2 into the page, the right hand rule at that point indicated a force toward the first wire. Considering wire 2 as the source of magnetic fields leads to an attractive force relationship between the two wires.