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EE 314 - Basic Electrical Engineering ELECTROMAGNETISM The Force Exerted on Magnetic Field It has been experimentally observed that, when a particle that has charge q and velocity v is in a region with a magnetic field B, a force acts on the particle that is proportional to q, to v, to B, and to the sine of the angle between the directions of v and B. When a particle that has a charge q and a velocity vS is in a region with a magnetic field B, the magnetic force F on the particle is: The magnetic field B in terms of the force exerted on a moving charged particle. The SI unit of magnetic field is the tesla (T). Right-hand rule for determining the direction of a force exerted on a charged particle moving in a magnetic field. If q is positive, then F, is the same direction with v X B. When a current-carrying wire is in a region that has a magnetic field, there is a force on the wire that is equal to the sum of the magnetic forces on the individual charge carriers in the wire. Thus, the total force on the wire segment is the number of charges in the wire segment is the number n per unit volume multiplie by the volume AL. Also, the current in the wire is I = nqvdA. Hence, the force can be written Torques on Current Loops and Magnets A current-carrying loop experiences no net force in a uniform magnetic field, but it does experience a net torque. F2 = F4 = IaB where: I = current through the conductor A = area of the loop B = magnetic field Now suppose that the uniform magnetic field makes an angle & < 90° with a line perpendicular to the plane of the loop Examples: 1) A proton moves perpendicular to a uniform magnetic field B at 1.00 X 10^7 m/s and experiences an acceleration of 2.00 X 10^13 m/s^2 in the +x direction when its velocity is in the + z direction. Determine the magnitude and direction of the field. 2) An electron has a velocity of 1.20 X 10^4 m/s (in the positive x direction), and an acceleration of 2.00 X 10^12 m/s^2 (in the positive z direction) in a uniform electric and magnetic field. If the electric field has a magnitude of 20.0 N/C (in the positive z direction), what can you determine about the magnetic field in the region? What can you not determine? 3) A wire having a mass per unit length of 0.500 g/cm carries a 2.00-A current horizontally to the south. What are the direction and magnitude of the minimum magnetic field needed to lift this wire vertically upward? 4) A conductor suspended by two flexible wires as shown has a mass per unit length of 0.040 0 kg/m. What current must exist in the conductor in order for the tension in the supporting wires to be zero when the magnetic field is 3.60 T into the page? What is the required direction for the current? 5) A long piece of wire with a mass of 0.100 kg and a total length of 4.00 m is used to make a square coil with a side of 0.100 m. The coil is hinged along a horizontal side, carries a 3.40-A current, and is placed in a vertical magnetic field with a magnitude of 0.010 T. (a) Determine the angle that the plane of the coil makes with the vertical when the coil is in equilibrium. (b) Find the torque acting on the coil due to the magnetic force at equilibrium. 6) A rectangular coil consists of N = 100 closely wrapped turns and has dimensions a = 0.400 m and b = 0.300 m. The coil is hinged along the y axis, and its plane makes an angle θ = 30.0° with the x axis. What is the magnitude of the torque exerted on the coil by a uniform magnetic field B = 0.800 T directed along the x axis when the current is I = 1.20 A in the direction shown? What is the expected direction of rotation of the coil?