iPad 10:56 AM o 100% 3. C+ 0.5/2 points I Previous Answers My Notes The unit of

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iPad 10:56 AM o 100% 3. C+ 0.5/2 points I Previous Answers My Notes The unit of magnetic flux is named for Wilhelm Weber. A practical-size unit of magnetic field is named for Johann Karl Friedrich Gauss. Along with their individual accomplishments, Weber and Gauss built a telegraph in 1833 that consisted of a battery and switch, at one end of a transmission line 3 km long, operating an electromagnet at the other end. Suppose their transmission line was as diagrammed in the figure below. Two long, parallel wires, each having a mass per unit length of 31.5 g/m, are supported in a horizontal plane by strings l 6.30 cm long. When both wires carry the same current I, the wires repel each other so that the angle between the supporting strings is 0 15.8 (a) Are the currents in the same direction or in opposite directions? O the same direction O opposite directions (b) Find the magnitude of the current 59.2 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out a intermediate results to at least four-digit accuracy to minimize roundoff error. A (c) If this transmission line were taken to Mars, would the current required to separate the wires by the same angle be larger or smaller than that required on the Earth? O larger smaller

Explanation / Answer

since it is balanced , ratios ll be equal hence

{T sin theta/2} / {T cos theta/2} = {Fb/L}/{mg/L}-----------(1)

also

Fb/L = IB sin theta = IB sin90 = IB

= uI^2/2pie*a

and

mg/L = lambda*g

also

a = 2l sin (theta/2)

hence substituting all these values in equation 1 we ve

tan (theta/2) = uI^2/[{2pie*2l sin theta/2}*(lambda *g)]

hence

I = sqrt [[4pie*l*lambda*g/u]*tan (theta/2)*(sin(theta/2))]

I = sqrt [[4pie*0.063*0.0315*9.8/4pie*10^-7]*tan (7.9)*(sin(7.9))] = 60.93 A

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