Laboratory Experiments on Currents and Magnetic Forces in Physics 132L, Lab Reports of Physics

Download Laboratory Experiments on Currents and Magnetic Forces in Physics 132L and more Lab Reports Physics in PDF only on Docsity! Phys 132L Spring 2009 Laboratory 10: Currents and Magnetic Forces A general feature of electromagnetism is that currents produce magnetic fields. This magnetic field can, in principle, be determined by applying the Biot-Savart law. In highly symmetric situations, such as that of the field at the center of a circular current, an expression for the magnetic field can be determined explicitly. Combining the Biot-Savart law and the Lorenz force law allows one to predict the force exerted by one infinitely long straight current on another which is parallel. This set of experiments investigates these predictions quantitatively. 1 Forces between Two Currents The force exerted by one current carrying wire on another parallel current carrying wire of the same length is F = µ0I1I2 2πd L (1) where I1 and I2 are the currents in the two wires, d is the distance between the centers of the wires and L the length of the wires. This relationship can be investigated using a current balance, whose essential working parts are two rigid parallel wires through which the same current is passed. The current balance is designed so that one of the upper wire is free to pivot and the lower wire is fixed. When currents pass through the wires in opposite directions the lower wire exerts force on the upper wire which causes it to pivot upwards. This can be counteracted by adding masses to the small balance pan on the upper wire, eventually returning the upper wire to its equilibrium position. When the balance is in equilibrium, the gravitational force due to the additional mass equals the force exerted by the lower wire on the upper wire. a) Equilibrium position and L : Set up the current balance with no additional mass in the pan. Let it come to rest and note the position of the reflected laser beam on the wall (the “equilibrium point”). Mark the equilibrium point. Measure and record the length of the upper wire. b) Determining d : The distance between the two currents can be measured by noting how far the reflected laser beam moves when the upper wire is completely depressed against the lower wire. Place a coin on the mass pan and measure the distance, ∆y, through which the beam moves away from the equilibrium point on the wall. Geometrical reasoning shows that the gap between the two wires is dgap = ∆y 2D b where D is the distance from the pivot point to the wall, and b is the distance from the pivot point to the wire. Determine dgap. Then d is dgap plus the width of one of the wires. Measure the width of one of the wires and use this to determine d. Verify your result with the instructor. The current balance is configured so that the currents through the two arms are opposite and of equal magnitude. Denote the magnitude of the current by I. c) Force vs. current: Place a 10mg masspiece in the balance pan. Adjust the current until the reflected light beam returns to the equilibrium point and then measure and record the current. Reverse the direction of the current through the apparatus (this should partially cancel the effects of the earth’s magnetic field) and again balance the arm and measure and record the current. Determine the average current and calculate the percentage difference between this and the predicted current. d) Repeat the previous part for three other values of mass in the balance pan. e) For each value of additional mass in the pan, calculate the force, F, exerted by the lower current on the upper current. Plot F vs. I2. Is the graph a straight line or not? How does this compare to the graph predicted by theory? f) Determine an expression, in terms of L, d and constants, for the slope of the graph of F vs. I2. Calculate a value of this, compare it to the slope of your graph and determine the percentage difference between the two. 2 Force Exerted by Current Carrying Coil on a Magnet: Determining the Earth’s Magnetic Field This experiment uses a circular current-carrying coil with N complete loops of wire. The magnetic field at the center of the loop points along the axis of the loop in a direction given by the right hand rule. The magnitude of the magnetic field at the center of the loop is given by B = N µ0I 2R (2) where R is the radius of the loop and I the current through the loop. This can be used in the following way to determine the earth’s magnetic field. a) Place the compass at the center of the loop and orient the loop so that the plane of the loop lies along the north-south direction. b) Suppose that current passes through the coil. Indicate the two possible directions of the magnetic field produced by the coil. In each case, sketch qualitatively the net magnetic field vector at the center of the loop, indicating the contributions from the earth’s magnetic field vector and the magnetic field vector produced by the coils. c) Adjust the current through the coil so that the compass needle deflects by about 20◦. Measure the current through the coil, determine the magnitude of magnetic field produced by the coil and use this to determine the magnitude of the earth’s magnetic field. d) Repeat the previous part for compass needle deflections of 30◦, 40◦, 50◦, and 60◦. 2