QJEEAdv12Ph1ae2: JEE Advanced 2012 Physics - Class 12 JEEAdv12Ph1ae2 Solution: A cylinder cavity of diameter a exists inside a cylinder of…

B_R = B_T $-$ B_C

R = Remaining portion

T = Total portion and

C = cavity

${B_R} = {{{\mu _0}{I_T}} \over {2a\pi }} - {{{\mu _0}{I_C}} \over {2(3a/2)\pi }}$ ..... (i)

${I_T} = J(\pi {a^2})$

${I_C} = J\left( {{{\pi {a^2}} \over 4}} \right)$

Substituting the values in Eq. (i), we have

${B_R} = {{{\mu _0}} \over {a\pi }}\left[ {{{{I_T}} \over 2} - {{{I_C}} \over 3}} \right]$

$= {{{\mu _0}} \over {a\pi }}\left[ {{{\pi {a^2}J} \over 2} - {{\pi {a^2}J} \over {12}}} \right]$

$= {{5{\mu _0}aJ} \over {12}}$

$\therefore$ $N = 5$