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Paragraph for Questions 1 and 2 When electric current in a material is proportional to the voltage across it, the material is said to be "ohmic", or to obey Ohm's law. A microscopic view suggests that how application of an electric field to a conducting material leads to an electric current, The current density (electric current per unit area, J

`=(I)/(A)`

can be expressed as:

`J=\sigma E`

. In the above equation, sigma

`\sigma `

is a constant called the conductivity of a material, E is the applied electric field. In complicated materials where the conductivity changes over the length of the conductor, the analysis is done by treating an infinitesimal quantity and integrating. Suppose we have a cylindrical conductor of radius r and length L . If it's resistivity is non uniform and varying as the position X from left end of the cylinder as given by the equation

`\rho =\rho _(0)(1+(x)/(l))`

. Find the ratio of electric field at

`x=l&x=(-)/(2)`

. Find the ratio of total resistance with resistance of left half.