A coaxial cable consists of alternating coaxial cylinders of conducting and insu

Question

A coaxial cable consists of alternating coaxial cylinders of conducting and insulating material. Coaxial cabling is the primary type of cabling used by the cable television industry and is also widely used for computer networks such as ethernet, because of its superior ability to transmit large volumes of electrical signal with minimum distortion. Like all other kinds of cables, however, coaxial cables also have some self-inductance that has undesirable effects, such as producing some distortion and heating.

Consider a long coaxial cable made of two coaxial cylindrical conductors that carry equal currents I = 2.35 A in opposite directions (see the figure); you may consider the insulating material between the two conductors to be simply air. The inner cylinder is a small solid conductor of radius a = 0.950 mm . The outer cylinder is a thin-walled conductor of radius b = 5.650 mm. This cable will be carrying high frequency AC signals; as a result, due to what is known as the "skin effect", the current I will flow down the (outer) surface of the inner conducting cylinder and back along the outer surface of the outer conducting cylinder. You may ignore any possible thickness of the outer cylinder.

(a) For r < a, how does the magnetic field strength vary with distance r from the central axis of the cable?

The field strength is independent of r.The field strength is proportional to r.    The field strength is proportional to 1/r.The field strength is proportional to 1/r2.The field strength is proportional to 1/r3.The relationship between field strength and r is more complicated than any expressed above.

(b) What is the value of the magnetic field strength for r = 0.475 mm?
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(c) For a < r < b, how does the magnetic field strength vary with distance r from the central axis of the cable?

The field strength is independent of r.The field strength is proportional to r.    The field strength is proportional to 1/r.The field strength is proportional to 1/r2.The field strength is proportional to 1/r3.The relationship between field strength and r is more complicated than any expressed above.

(d) What is the value of the magnetic field strength for r = 2.517 mm?
T

(e) What is the value of the magnetic field strength for r = 4.083 mm?
T

(f) For r > b, how does the magnetic field strength vary with distance r from the central axis of the cable?

The field strength is independent of r.The field strength is proportional to r.    The field strength is proportional to 1/r.The field strength is proportional to 1/r2.The field strength is proportional to 1/r3.The relationship between field strength and r is more complicated than any expressed above.

(g) What is the value of the magnetic field strength for r = 11.300 mm?
T

(h) Now consider the cable to be a part of a simple complete circuit formed by a connecting a battery between the inner and outer conductors at one end of the cable, while at the other end the connection between the inner and outer conductors is made with a short metal wire. The battery is then driving the 2.35-A current in the cable. Assume the cable is 70 meters long. Do the necessary integral to calculate the magnetic flux through this simple circuit; you may ignore any part of the flux which is through any part of the circuit which is outside of the cable (i.e.those parts of the circuit which include the battery and the short connecting wire). To make your work as simple as possible, choose the simplest possible surface which bounded by the conducting circuit. HINT: the area of this "simplest possible surface" is the cable length times the quantity (b - a).
Wb or T

Explanation / Answer

(a) The field strength is independent of r

(b) 0

(c) The field strength is proportional to 1/r.

(d) and (e) Use B = (mew*current)/(2*pi*r)

(f) The field strength is independent of r

(g) 0

(h) Magnetic flux = [(mew*current*length)/(2*pi)]* ln(b/a) ===> just plug in your values here

(i) Inductance = Magnetic flux / current =====>> plug in values

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