The figure shows a cable through which a current I flows, which is composed of a straight segment of length L and parallel to the z axis, then a semicircular segment of radius R and contained in the xy plane, and then another segment of length L, parallel to the x axis. In all space there is a uniform magnetic field B (with arrow) = Bz (z with hat), find the total magnetic force on the three segments of the wire. (The answer must be expressed in terms of I, B, L and R)
Ampere Circuital Law
Ampere's Law states that "for any closed loop path, the sum of the length elements times the magnetic field in the direction of the length element is equal to the permeability times the electric current enclosed in the loop.”
Current Density
To design the electrical and electronic system, the current density is an important factor. The designer current level is the factor on which the circuit performance depends and with the help of the dimensions of the conducting current the current density is then determined. For instance, despite the lower current demanded by smaller devices as integrated circuits are reduced in size, there is a type of trend in achieving the higher device number in even smaller chip areas. The current density is increased in this region at higher frequencies because the conducting region in a wire becomes confined and this is known as the skin effect. The consequences increase as the current densities become higher.
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