A cylindrical conductor of radius $'R'$ carries a current $'i'$. The value of magnetic field at a point which is $R/4$ distance inside from the surface is $10\, T$. Find the value of magnetic field at point which is $4\,R$ distance outside from the surface
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(b) Magnetic field inside the cylindrical conductor
${B_{in}} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2ir}}{{{R^2}}}$ ($R$ = Radius of cylinder, $r$ = distance of observation point from axis of cylinder)
Magnetic field out side the cylinder at a distance $r'$ from it’s axis ${B_{out}} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2i}}{{r'}}$
$ \Rightarrow \frac{{{B_{in}}}}{{{B_{out}}}} = \frac{{rr'}}{{{R^2}}} \Rightarrow \frac{{10}}{{{B_{out}}}} = \frac{{\left( {R - \frac{R}{4}} \right)\;(R + 4R)}}{{{R^2}}}$ $ \Rightarrow {B_{out}} = \frac{8}{3}\,T$
${B_{in}} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2ir}}{{{R^2}}}$ ($R$ = Radius of cylinder, $r$ = distance of observation point from axis of cylinder)
Magnetic field out side the cylinder at a distance $r'$ from it’s axis ${B_{out}} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2i}}{{r'}}$
$ \Rightarrow \frac{{{B_{in}}}}{{{B_{out}}}} = \frac{{rr'}}{{{R^2}}} \Rightarrow \frac{{10}}{{{B_{out}}}} = \frac{{\left( {R - \frac{R}{4}} \right)\;(R + 4R)}}{{{R^2}}}$ $ \Rightarrow {B_{out}} = \frac{8}{3}\,T$
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