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Summary The direction in which a current carrying wire is forced when it is in a magnetic field can be determined by using a right hand rule. Step 1: First orient your hand so that the outstretched fingers point in the direction of the conventional current (away from positive towards negative). Step 2: Bend you fingers so that they point in the direction of the magnetic field lines (from the N towards S on a magnet). To do this, you may have to rotate you hand and arm about the wrist until they do point along the magnetic field when bent. Step 3: Once your hand is oriented in the proper direction, extend your thumb. It will point in the direction of the force on the wire. To show directions into the page and out of the page, the dot symbolizes a vector pointing out of the page toward the reader and the "x" symbol symbolizes a vector pointing into the page away from the reader. The force on the current carrying wire in a magnetic field can be found using F = BIL. If the current and the magnetic field are not at right angles to each other, then the component of current that is perpendicular to the field (or the component of field that is perpendicular to the current) must first be determined. For a charged particle to experience a force in a magnetic field, two important conditions must be met. 1. The charge must be moving. A magnetic field will not influence the motion of a charged particle at rest. 2. The velocity of the moving charge must have a component that is perpendicular to the direction of the magnetic field. To determine the direction of the force that a moving charged particle experiences in a magnetic field, we use the right hand rule discussed earlier. Step 1: First orient your hand so that the outstretched fingers point in the direction of motion of a positive charge. Step 2: Bend you fingers so that they point in the direction of the magnetic field lines. Step 3: Once your hand is oriented in the proper direction, extend your thumb. It will point in the direction of the force on the positively charged particle. The force that a charged particle experiences as it moves through a magnetic field is given by F = qvB. If the particle is moving at some an angle other than 90, the component of velocity perpendicular to the magnetic field must be determined. A charged particle moving in a constant magnetic field moves in a circle. In this case the centripetal force and the magnetic force on the particle are equal. 2 v m=qwB S R q mv = gBR. yCalculating the Force on a Charged Particle Moving in a Magnetic Field Earlier in the lesson we saw that the magnitude of the force on a current carrying wire in a magnetic field was F = BIL sin. The sin is necessary to find the component of the current perpendicular to the field. From this equation, we can derive an equation showing the force on a charged particle moving in a magnetic field. The current flowing through a wire is the total charge in coulombs moving per unit time in seconds. =4 t If we let t be the time for a charge g to travel a distance L in a magnetic field B, then L = vt, where v is the velocity of the particle. Substituting into the equation for force, F =B(%}vt)sin6 = Bgv sinf Another way to write this is F = qvB sin@ For example, if a charge of 1.0 C moves at 5.0 m/s in a magnetic field of 6.00 T at an angle of 30.0 with respect to the magnetic field lines, then the force on the charged particle is F = (1.0 C)(5.0 m/s)(6.00 T)(sin 30.00) = 15 N Also, if we apply the right hand rule, the component of the velocity is up while the magnetic field is to the right, so the direction of force is into the page. :} Direction of Motion of a Charged Particle in a Magnetic Field We have seen in earlier work that when a charged particle enters an electric field, it experiences a force. When a charged object enters a magnetic field, it also experiences a force. There are two very important conditions that must be met for a charged particle to experience a force in a magnetic field. 1. The charge must be moving. A magnetic field will not influence the motion of a charged particle at rest. 2. The velocity of the moving charge must have a component that is perpendicular to the direction of the magnetic field. To determine the direction of the force, we use the right hand rule discussed earlier for the force that a magnetic field exerts on a straight current carrying wire. The three steps are repeated here for the motion of a charged particle in a magnetic field. Step 1: First orient your hand so that the outstretched fingers point in the direction of motion of a positive charge. Step 2: Bend you fingers so that they point in the direction of the magnetic field lines. Step 3: Once your hand is oriented in the proper direction, extend your thumb. It will point in the direction of the force on the positively charged particle. Earlier in the lesson, we looked at a diagram showing the force on a wire moving in a magnetic field. The same diagram could be used to illustrate the force on a positively charged particle moving in a magnetic field. The vector to the right would represent the initial direction of motion of the charged particle, that is its initial velocity. This particle would be forced into the page. The crosses show the direction of the force. X represents the force direction If the particle was negatively charged, it would be forced in a direction opposite to that of a positive charge. In the above case, a negative particle would be forced out of the page. Note that in the case where the particle moves parallel to the magnetic field, there is no force on the particle. Question(s): 1. The physics of an airplane moving through the earth's magnetic field. An airplane flies through the earth's magnetic field at a speed of 200.0 m/s. As it does so, it acquires a negative charge of 100.0 C. Assume that the plane travels in a perpendicular path through the magnetic field of the earth that has a magnitude of 5.0 x 1072 T in that region. a) What is the maximum magnetic force on the charges on the plane? b) Suppose that the direction of the magnetic field is vertically down on the plane, and that the plane is moving from west to east. In what direction what the electrons be forced? 2. The physics of an alpha particle moving in a magnetic field. What is the radius of the path taken by an alpha particle (HeZ* ion of charge 3.2 x 1017 C) and mass 6.7 x 1027 kg) injected at a speed of 1.5 x 107 m/s into a uniform magnetic field of 2.4 T, at right angles to the field