Answer:
Let us carry out a small activity. Take a coin. We know that coin is circular in shape. Now place another coin on the first coin and so on. You will see that when you place such coins, the structure that you get is a cylinder, which is three dimensional. Let us learn about the volume of a Cylinder in this chapter.
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If the current density as a function of distance 'rr' from the axis of a radially symmetrical parallel stream of electrons is given as \displaystyle j(r)=\dfrac{xb(\alpha+1)}{\mu_0}r^{\displaystyle (\alpha-1)}j(r)=μ0xb(α+1)r(α−1) if the magnetic induction inside the stream varies as B=br^\alphaB=brα, where bb and \alphaα are positive constants. Find 'xx'
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The current density \vec{j}j inside a long, solid cylindrical wire of radius a =12mma=12mm is in the direction of the central axis and its magnitude varies linearly with radial distance rr from the axis according to J=\dfrac{J_0r}{a}J=aJ0r where J_0=\dfrac{10^5}{4\pi }\dfrac{A}{m^2}J0=4π105m2A. The magnitude of magnetic field at r=\dfrac{a}{2}r=2a in \mu TμT is:
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If I_{o}Io is the current through the cylinder with constant current density (a/R), then the net current through the cylinder is :
