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New York University - PHYSICS V85.0012Physics2Lab6-7-9 on current balance

1.lab 6 Objective The purpose of this lab is to measure the permeability of free space. This will be done using a current balance apparatus and laser to verify the force between two wires, which is... proportional to the permeability constant. Description Two wires carrying current near each other will experience force due to the other wire. The force that the wires feel is proportional to the products of the currents. The current balance apparatus has a wire that can pivot freely up and down, and a coil parallel to the freely moving wire right under it. These are connected in series, and therefore the same current passes through them both. But, the current is passing through them in opposite directions. This gives a net force of repulsions between the two. The laser is adjusted and two marks will be made, one for when two wire and coil are .1 mm apart and one for .2 mm apart. Weights will be added to the single wire, and since it moves freely, the current and repulsive force are adjusted to get the laser to hit the premade points. This is repeated with different weights and will be used to determine force as a function of current. Theory Two parallel wires are carrying current in opposite directions. This will lead to a net force of repulsion between the two. Since one wire is able to freely move up and down, the bottom coil will repel the top wire up. Force per unit length of one wire on another can be written as F= 2 μ0 IA IB 4 πD , where IA and IB are the currents in the two wires. This equation is for infinitely long wires. For wires of length L, force per unit length becomes F= 2 μ0 IA IB L 4 πD . Since in this experiment the two currents are the same and the coil has N = 10 turns, the equation is rewritten again as F=2 μ0 N I2L 4 πD . This can be derived into two equations for the two different distances used in this experiment. F1=2 μ0N I12 L 4 π(a+b) and F 2= 2 μ0 N I22L 4π (2a+b) . Plotting a graph of force vs current squared gives two slopes, F 1 I 1 2=S1 and F 2 I 2 2=S2 . These two equations are used to solve for b = a(2S2−S1) S 1−S2 . Solving for b now gives the value of µ0/4π. μ0 4 π = S1(a+b) 2NL Data and calculations a = .1 mm = 0.001m Weight (mg) Force (N) Current (amps) Current2 (Amps) 100 .98 Unable to measure 150 1.47 3.17 10.05 2.lab 7 1. Objective The goal of this experiment is to examine the relationship between current and the magnetic force through the wire. We will also verify that the force between two wires is proportional to the product of the currents, and estimate the proportionality constant involved. 2. Description A single horizontal U shaped rod or wire is pivoted so that it can move freely up and down. Below the wire is a long 10 turn rectangular coil whose long sides are in horizontal plain and run parallel to the single wire. One long side of the coil is a lot closer to the single wire than the other long side of the coil. The single wire and coil are connected in series and a current flows through them so that the current is flowing in the opposite directions for the single wire rod and the nearby long side of the coil. The net force between wire and coil is a repulsion. In section 6, with zero current, the vertical position of the single wire is adjusted to a certain value. A weight is then added to a pan on the single wire and a DC (constant) current established so that the position of the single wire returns to its initial value. This procedure is repeated for a number of weights. This determines the force on the single wire as a function of the current. The apparatus that was used includes the current balance apparatus, laser on tripod, paper and tape, Fluke multimeter, leads, 9 V DC from wall strip, 5 Ω 9.2 A rheostat, two 6 inch flat 1 mm thick rulers, weights (50 mg, 100 mg, 200 mg). The long rectangular coil is fixed in position. The single wire is held by two rods that are attached to a pivot arm that pivots on two knife edges. This allows the single wire to freely move in a vertical plane toward and away from the coil. This single wire assembly has a balance adjustment weight that allows the equilibrium vertical position of the single wire to be adjusted. In the center of the single wire there is a pan where you will be placing the fractional masses. There is a mirror attached to the pivot arm. A laser beam is directed onto the mirror and then reflected back to a piece of paper taped to the front of the laser. This allows you to return the single wire to a given position with great accuracy. The “period adjustment weight” changes the oscillation period of the single wire. Moving this weight down makes the period of oscillation longer, and lengthens the times necessary for the wire to stop oscillating. It also serves to make the equilibrium position of the wire stable, since it is located below the pivot points. The lower this weight is, the more stable the mechanical equilibrium of the wire. There is a “centering rod” that has two knobs at the ends and two off-set points. When the centering rod is rotated, the two points fit into two tapered holes in the bottom of the pivot arm, and one can lift the pivot arm a bit. When the pivot arm is lowered back down, the knife edges should be centered on their supports. This should be done gently so the knife edges don’t become damaged. In this experiment, two small plastic rulers will be provided that are quite close to 1.0 mm thick. They are used as spacers to set the distance d between the single wire and coil. A metal plate attached to the pivot arm is positioned in the gap of a small permanent magnet. As the pivot arm swings back and forth, this arrangement provides eddy current damping. A rheostat is a variable resistor. It consists of resistance wire wound on a cylindrical form so that the resistance wire form 3.lab 9 1 Objective and Theory For this lab, our objective was to essentially measure the amount of force that it took to generate the same force as a varying array of masses. The objective of this lab is to calculate ε0 by using a known voltage, cross-sectional area, and separation distance from plates. We use a laser beam and the constant force of gravity in order to ensure that we know the correct force that this specific voltage is exerting on the capacitor plates. The theory behind all of this involved Coulomb’s law, with the force equal to the charges, which in this case was currents, and the distance. [Show More]

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