One straight way to measure a magmatic field\'s strength is to a rotating coil p
ID: 1538204 • Letter: O
Question
One straight way to measure a magmatic field's strength is to a rotating coil placed in the field. (This method was widely used by physicists until late in the 20th century, when sensitive Hall-effect sensor became available.) Suppose that we have an N-turn coil shaped like a circular loop with radius R turning at an angular rate omega in a nearly uniform magnetic field B. The coil rotates around an axis that goes through the coil's diameter and is perpendicular to the field you want to measure. You connect the ends of the coil (through slip rings) to an AC volt-meter that measures the amplitude of the alternative emf induced in the coil as it rotates in the field. Find an expression for induced emf that the ammeter measures in terms of N, R, | omega|, | B |, and time t. Suppose that you want the emf's amplitude to be exactly 1.00 V in a 1.00-T field. You also want your Coll to be less than 1.6 cm in diameter, and the motor turning the coil rotates at 60.0 turns/s. Find the smallest value of N and the corresponding value of R that delivers the desired emf-to-field ratio.Explanation / Answer
a)
EMF induce
E = N x 3.14 x R^2 x w xB Cos wt
b)
substituting the values we get
N R^2x 3.14 x 2 x3.14x60 = 1
NR^2 = 8.45 x 10^-4
smallest N
N = 13.2
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