a Reasonabien Can Current in a 20-A Wire in a Home Induce A 100-turn coilofradiu

Question

a Reasonabien Can Current in a 20-A Wire in a Home Induce A 100-turn coilofradius 1.0 cm is 1.0 m from a very long straight wire that carries a current dap A volta e inducedint Both the wire andt Hollare in the plane ofthe paper Determine the aer averg (20 A) sin [2T (60 Hz) t]. Both the wire and the indeed in the coil. (Note that 60 -60 cycles.) PICTORIAL REPRESENTATION Complete the sketch at the right, inchuding any other information that will clarify the problem. Then, describe briefly below a strategy for solving the problem a) What is Bs 1 m from the wire? b) what is .m through the coil? 1.26 × 10-9 Wb ACD Find using the approximation V. dD dt e) Find Vr ALPS Kt, Box 4013, University Pk Las Crumn, NM 88003 IX-19 (Magnetism) A FIPSE Project

Explanation / Answer

a)

magnetic field due to wire at 1 m = Bwire = uo*I/(2*pi*r)

Bwire = 4*pi*10^-7*(20)sin(2pi*60*t)/(2*pi*1)

Bwire = 4*10^-6*sin(2*pi*60*t)

(b)

magnetic flux phi = N*Bwire*A

A = pi*r^2 = pi*0.01^2 = 3.14*10^-4

flux = 100*12.56*10^-10*sin(2*pi*60*t)

flux = 1256*10^-10*sin(2*pi*60*t)

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(c)

Vavg = dphi/dt = 1256*10^-10*cos(2*pi*60*t)*(2pi*60)

Vavg = 4.735*10^-5*cos(2pi*60*t)

=======================

(d)

Vpeak = 4.735*10^-5 V

===================

(e)

Vrms = (Vpeak)/sqrt2 = 3.35 V

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