#1 The diagram on the left shows a solenoid in cross section. Compute the field

Question

#1 The diagram on the left shows a solenoid in cross section. Compute the field strength if the solenoid has a length of 55 cm, a radius of 17 cm, 650 loops and a current of 1.7 A. In the interior of the solenoid, there is a square loop -- oriented so that its normal is along the B field direction. It has sides of 5.0 cm length and a resistance of 68 Ohm. What current is induced in this loop as the current in the solenoid is increased uniformly from the original 1.7 A to 2.8 A in 215 ms? Sketch the direction of the current. A small generator is designed to provide standard AC electricity (V_mm = 115 V, f=60 Hz). The coil has 85 loops and an area of 0.0263 m^2. At what angular frequency, omega, must

Explanation / Answer

1 a) Magnetic Field B = B = 0 I N / L =4 * pi x10^-7 x1.7 x 650 / 0.55 = 2.52 x 10^-11 A/m

1 b) Magnetic Field B when current is 2,8 A = 4 * pi x10^-7 x2.8 x 650 / 0.55 = 4.15 x 10^-11 A/m

induced emf= e= d(BA)/dt = pi * r^2 x dB/dt = 3.14 x (0.17)^2 x (4.15-2.52) x 10^-11/2.15 x 10^-3 =6.88 x 10^-10 V

I = e/R = 1.012 x 10^-11 A

2) omega = 2 * pi * f = 2* 3.14* 60 = 376.8 radian/sec

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