A bar magnet is dropped through a long vertical copper tube. (Assume that the magnet is smaller than the inner diameter of the tube and is not initially touching the tube). What effect will the pipe have on the magnet's fall through the tube? The magnet will fall slower as a result of its kinetic energy getting stored as magnetic energy in its magnetic field. The magnet will fall faster as a result of the increased magnetic flux, which will manifest as a corresponding increase of kinetic energy. The magnet will fall slower as a result of the magnetic repulsion of eddy currents The magnet will fall faster as a result of the magnetic attraction between the tube and the magnet, which will cause a net downward force The increased friction caused by the attraction between the magnet and the tube will slow down the fall of the magnet The tube will have no effect on the fall of the magnet

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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.