Electrical measurementsA laboratory manual . l be in it, with its centre at 0. Letthe needle be deflected through an angle ^. Then twoforces act upon each pole. One is SfSm^ \ due to thehorizontal component of the earthsfield; the other, due to the current 7, isat right angles to the plane of the coil, and equals , where r is the mean radius of the coil, consisting of a single turn of the conductor, and ni is the strength of pole of the needle. For equilibrium the moments of these two forces, or the moments of the two ^^ ^^ couples, due to the pairs of equal forces acting on the two ends of th
Electrical measurementsA laboratory manual . l be in it, with its centre at 0. Letthe needle be deflected through an angle ^. Then twoforces act upon each pole. One is SfSm^ \ due to thehorizontal component of the earthsfield; the other, due to the current 7, isat right angles to the plane of the coil, and equals , where r is the mean radius of the coil, consisting of a single turn of the conductor, and ni is the strength of pole of the needle. For equilibrium the moments of these two forces, or the moments of the two ^^ ^^ couples, due to the pairs of equal forces acting on the two ends of the needle, must be equal to each other. The moment of the orienting magnetic force due to the earths field is &6ml sin ^, where I is the half length of the needle. The moment of the deflecting force is L cos c7. Hence, r ?^^^ cos d = &S^l sin ^. ^ co^ a r H 5H. ^ The m and I cancel out. The deflection is thereforeindependent of the strength of pole; but the lengthis limited for a reason already given. From this equation 1= ml- tan 120 ELECTRICAL MEASUREMENTS. For n turns of wire, where n is only a very smallnumber, and where the n turns may be consideredcoincident, J=a?~tan(9. TT 277?? The fraction ^^, or , is called the constant of the r r galvanometer. It depends upon the dimensions and the number ofturns of wire in the coil, and equals the strength of fieldproduced at the centre by unit current flowing throughthe coil. If this constant be denoted by (x, then J=^%.an^ (1) G- The equation may be written simply J=^tan^ (2) The current is measured in units. The num-ber of amperes is 10 times as great. When the constantof the galvanometer is determined from its dimensions,equation (1) must be used; when it is determined by silveror copper electrolysis, equation (2) is more convenient. 63. Influence of Errors of Observation. — The effect of an error in reading the deflection of the needleof a tangent galvanometer will be least relative to Iwhen 6 = 45°. This may be de
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