WRITTEN HOMEWORK ASSIGNMENT #6 DUE MARCH 25 Written Question #1: In the figure,
ID: 1444314 • Letter: W
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WRITTEN HOMEWORK ASSIGNMENT #6 DUE MARCH 25 Written Question #1: In the figure, a compass sits 1.0cm above a wire in a circuit containing a 1.0 F capacitor charged to 50 V. a 2.02 resistor, and an open switch. Initially, the compass is limed up with the earth's magnetic field. The switch is then closed, so there is a current in the circuit, and the switch remains closed until the capacitor has completely discharged. a. At the position of the compass, what is the direction of the magnetic field due to the current in the wire after the switch is closed? (Assume that the compass is only affected by the field created by the current in the wire that is directly below it.) b. At the position of the compass, what is the magnitude of the magnetic field due to the current in the wire at the following times after the switch is cksed? (Fill in the table to help with your calculations. The switch is closed at t 0 s.) llow does this compare with the magnitude of the field of the earth? Use 50uT for the magnitude of the earth's field. c. Describe how the compass orientation changes right after the switch is closed, and how the compass orientation changes for the next ten seconds. Wire's Fraction of Earth's Time, t(s) Current, 1 A Field. B(I) Field, B/LEExplanation / Answer
V = IR
V(t) = Voe^[-t/RC]
I(t) = [Vo/R]e^[-t/RC]
a. Direction of magnetic field when the switch is closed = right to left (parallel to the plane of the paper)
b. I(0) = [50/2] = 25A
I(2) = 25e^[-2/2*1] = 9.19A
I(4) = 25e^[-2] = 3.383A
I(6) = 25e^[-3] = 1.244A
I(10) = 25e^[-5] = 0.168A
Now, B = 2kI/a = 2*10^-7 * I / 10^-2 = 2*10^-5 I T
B(0) = 500 mu T
B(2) = 183.8 mu T
B(4) = 67.76 mu T
B(10) = 3.36 mu T
Fraction of earth's macnetic field
B(0)/E = 10
B(2)/E = 3.676
B(4)/E = 1.3552
B(10)/E = 0.0672
c. Compass deflection reaches maximum after the switch is closed and then it keeps osscillating with decreasing amplitude finally to rest on its mean position again
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