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THE CURRENT BALANCE OBJECT To measure the mutual force between two parallel electric currents with the current balance. APPARATUS Current balance telescope and scale, Variac and transformer, precision ac ammeter (0-10, 0-20 amps), set of milligram analytical weights (0-350 mg in 50 mg steps), spirit level, 2-meter stick equipped with caliper jaws, micrometer caliper, cross section paper. (The manufacturer’s “instructions” for operating the current balance are required for reference.) THEORY The ampere, MKS system, is defined as “that unvarying current which, if present in each of two parallel conductors of infinite length and one meter apart in empty space, causes each conductor to experience a force of exactly 2 x 10-7 newton per meter of length”. In the experiment, Fig. 1, an alternating current (r.m.s. value is equivalent to an “unvarying current”) in two conducting rods A, B each of length L connected in series electrically produces mutual repulsive forces of equal magnitude F on the rods. The upward force F on rod A is balanced by a weight placed upon the small pan W. Balance of the upward electromagnetic force by the downward weight is observed with a telescope and scale. F = 2 x 10-7 d L I newtons = 2 d LI rms 2 0 2 π μ , (1) where d is distance between the axes of rods A and B when the balance is in the zero-current equilibrium position. d=do + 2r, do = distance between wires , r = radius of each wire measured with micrometer. 29
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PROCEDURE: 1. With Variac switch “off” and the Variac plug disconnected from the ac outlet receptacle, plug the transformer into the Variac. Using wires, connect the transformer output to the current balance rods A, B and the AC ammeter in series. The ac ammeter uses the lower range. The hookup wires connected to the posts of the current balance apparatus should be brought out perpendicular to the moving frame of the apparatus to minimize interaction between hookup wires and the frame. 2.
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