An aluminum ring of radius r, = 5.00 cm and a resistance of 3.25 x 10* A is placed around one end of a long air-core solenoid with 1 010 turns per meter and radius r = 3.00 cm as shown in the figure below. Assume the axial component of the field produced by the solenoid is one-half as strong over the area of the end of the solenoid as at the center of the solenoid. Also assume the solenoid produces negligible field outside its cross-sectional area. The current in the solenoid is increasing at a rate of 270 A/s. (a) What is the induced current in the ring? A (b) At the center of the ring, what is the magnitude of the magnetic field produced by the induced current in the ring? (c) At the center of the ring, what is the direction of the magnetic field produced by the induced current in the ring? O to the left O to the right O upward O downward

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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.