Imagine one day you are unlucky enough to be living under an enormous high-volta
ID: 1264694 • Letter: I
Question
Imagine one day you are unlucky enough to be living under an enormous high-voltage power line. You can hear the line buzzing at 60 Hz, which makes you think back to your favorite first-year class on electricity and magnetism. If the currents are oscillating, you know that the magnetic field around the lines must be changing, so from Faraday?s Law a coil of wire placed nearby would have a current induced within it. a. If you wanted to power your 120 V (rms) toaster, how many turns would you need use in a coil with a 2 m diameter? Let's assume the magnetic field nearby has a peak strength of 100 MuT and your coil is oriented for maximum induction. (Assume a sinusoidal time dependence for your magnetic field.) b. How long of a wire would you need? c. If you're using standard copper household wire with a diameter of 2.05 mm (not nearly thick enough for this application, by the way) and the density of copper ?s 8.96 g/cm3, how much would the coil weigh? What would be its resistance if Rho copper = 1.68 X 10^-8 omega . m?Explanation / Answer
induced emf is defiend as the rate of change of magnetic flux
in mathematical form,
induced emf e = NAdB/dt or NABW or NA dB/dt cos theta
where A = area = pi r^2
N = no. of turns = ?
W = angular frequency = 2pi f
dB/dt = rate of change of magnetic field
B = magnetic field = 100 e-6 T
so
No. of turns N = emf/(AB W)
N = 120/(3.14* 1*1* 100 e-6*2*3.14* 60)
N = 1014.24 turns
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part B :
one tuns has a length of 2pir = 2*3.14 *1
= 6.28 mm
1014.23 turns will have a length of 6.28 * 1014.23
L = 6369.3644 m
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part C:
apply Density D = mass/Volume
here Voilume = AL
where A is area and L is lengt
so
also Resistance R = Rho L/A
R = 1.67 e -8 * 6369.3644/(3.14 * 1.025e-3 *1.025 e-3)
R = 32.24 ohms
SO Volume V = AL = 3.14 * 1.025 e-3 *1.025 e-3 *6369.3644
V = 0.021 m^3 = 0.021 *10^6 cm^3
so mass = DV
m = 8.96 * 0.021 e 6
m = 188.16 kgs