Two concentric coils each of radius equal to $2\pi \,{\rm{ }}cm$ are placed at right angles to each other. $3$ $ampere$ and $4$ $ampere$ are the currents flowing in each coil respectively. The magnetic induction in $Weber/{m^2}$ at the centre of the coils will be $({\mu _0} = 4\pi \times {10^{ - 7}}\,Wb/A.m)$
AIEEE 2005,AIIMS 2008, Medium
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(a)${B_{net}} = \sqrt {B_1^2 + B_2^2} $ $ = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\pi }}{r}\sqrt {i_1^2 + i_2^2} $
$ = {10^{ - 7}} \times \frac{{2\pi }}{{2\pi \times {{10}^{ - 2}}}}\sqrt {{{(3)}^2} + {{(4)}^2}} = 5 \times {10^{ - 5}}\,wb/{m^2}$
$ = {10^{ - 7}} \times \frac{{2\pi }}{{2\pi \times {{10}^{ - 2}}}}\sqrt {{{(3)}^2} + {{(4)}^2}} = 5 \times {10^{ - 5}}\,wb/{m^2}$
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