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Wagih Ghobriel

EXPERIMENT THE CURRENT BALANCE Introduction: A current-carrying wire will create a magnetic field in the space around it. If a second current- carrying wire is placed in this magnetic field, it will experience a magnetic force. Two parallel wires carrying currents in the same direction attract each other. As shown in Fig.1, a B is the magnetic field at wire b d a produced by the current in wire a. F ba the resulting force acting on wire b Fba because it carries current in field B . i b a a Parallel currents attract, and antiparallel currents repel. We can write: L F bai LbB a ib L where vectors L and B aae perpendicular, and Ba(due to ia) F  i LB sin90  o  oi a b Figure 1: Parallel currents attract, and ba b a 2d antiparallel currents repel where  io7 constant, called the permeability constant, whose value is defined to be exactly o=410 T.m/A, d is the distance between the two wires (center to center), and L is the length of the wires. The force acting between currents in parallel wires is the basis for the definition of the ampere, which is one of the seven SI base units. The definition, adopted in 1946, states that: The ampere is that constant current which, if maintained in two straight, parallel conductors of infinite length, of negligible circular cross se7ion, and placed 1 m apart in vacuum, would produce on each of these conductors a force of 210 Newtons per meter of length. Based on the above equation, the force F between two long parallel conductors each carrying a current, I, is given from the definition of the ampere by:  L F  o. .I 2 . (1) 2 d If d is kept constant, Eq.(1) can be written F = K I 2 (2) where K = 210 7( L / d ). (3) 2 Therefore, under the conditions of constant d, a plot of F vs. I should produce a straight line. The value of K can be determined from the slope of this line. This measured value of K can be used to compute  woich, in turn, can be compared with the exact value:  =4o10 T.m/A. Apparatus: The schematic diagram of the current balance setup is shown in Fig.2. The relevant current- carrying conductors are the upper and lower bars. Current will flow through the upper bar in one direction and then through the lower bar in the opposite direction. This will result in a repulsive magnetic force between the two bars. The lower bar is fixed in position, however, the upper bar is attached to a pivoting beam which allows it to “rotate” away from the lower bar in response to the magnetic force, as mentioned in the introduction. This force can be measured by balancing it against the gravitational force acting on a small mass placed on the weight pan of the upper bar, as shown. upper bar adjustment thumb screws mirror beam lift counter- weight weight pan upper bar lower bar knife edge lever arm lower bar beam lift adjustment thumb screws wooden base Figure 2: Schematic diagram of the current balance Use the leveling screws to make the base of the apparatus firm and level. Adjust the counterweight until the separation of the bars is approximately 0.5 cm. Check that the beam lift (which raises the knife edges off their supports) engages and releases without shifting the position of the knife edges. When not in use the lift should be rotated away so that it is not in contact with the beam. To align the two bars and to examine them for straightness, place a coin on the weight pan to bring the bars into contact. Thumb screws on each front post permit either end of the lower bar to be raised or lowered. Similar thumb screws on the beam at the rear permit either end of the upper bar to be moved forward or backward. By careful adjustment the two bars should be aligned as accurately as can be determined by the unaided eye when viewed from the front and from the top. When viewed from the front, with a white paper behind the bars, the two bars may appear to be slightly lacking in straightness. If this is very serious, it should be corrected by gently bending one bar or the other by hand until both app
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