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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 a is the magnetic field at wire b d produced by the current in wire a . F ba is the resulting force acting on wire b F ba because it carries current in field B a . i a b Parallel currents attract, and antiparallel currents repel. We can write: L F ba = i b L × B a i b L where vectors L and B a are perpendicular, and B a (due to i a ) d i i L LB i F b a o o a b ba π μ 2 90 sin = = Figure 1: Parallel currents attract, and antiparallel currents repel where o is a constant, called the permeability constant, whose value is defined to be exactly o =4 π× 10 7 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 section, and placed 1 m apart in vacuum, would produce on each of these conductors a force of 2 × 10 7 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: 2 . . 2 I d L F o = . (1) If d is kept constant, Eq.(1) can be written F = K I 2 (2) where K = 2 × 10 7 ( L / d ). (3) Therefore, under the conditions of constant d , a plot of F vs. I 2 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 o which, in turn, can be compared with the exact value: o =4 π× 10 7 T.m/A.
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Apparatus: The schematic diagram of the current balance setup is shown in Fig.2. The relevant current-
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This note was uploaded on 04/01/2011 for the course PHY 135 taught by Professor Wagihghobriel during the Spring '11 term at University of Toronto- Toronto.

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