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(d) Directions of currents in two parts are different, so directions of magnetic fields due to these currents are opposite. Also applying Ohm&rsquo;s

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Zero for all values of $	heta $

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(d) Directions of currents in two parts are different, so directions of magnetic fields due to these currents are opposite. Also applying Ohm&rsquo;s law across $AB$
${i_1}{R_1} = {i_2}{R_2} \Rightarrow {i_1}{l_2} = {i_2}{l_2}$     $\left( {\;R = ho \frac{l}{A}} ight)$
Also ${B_1} = \frac{{{\mu _o}}}{{4\pi }} 	imes \frac{{{i_1}{l_1}}}{{{r^2}}}$ and ${B_2} = \frac{{{\mu _o}}}{{4\pi }} 	imes \frac{{{i_2}{l_2}}}{{{r^2}}}$    ($\;l = r	heta $)
$	herefore \,\frac{{{B_2}}}{{{B_1}}} = \frac{{{i_1}{l_1}}}{{{i_2}{l_2}}} = 1$
Hence, two field induction&rsquo;s are equal but of opposite direction. So, resultant magnetic induction at the centre is zero and is independent of $	heta $.

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