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Q.

Two infinite length wires carry currents 8A and 6A respectively and placed along X and Y-axis. Magnetic field at a point  P(0,0,d)m will be

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a

\frac{{10{\mu _0}}}{{\pi d}}

b

\frac{{7{\mu _0}}}{{\pi d}}

c

\frac{{14{\mu _0}}}{{\pi d}}

d

\frac{{5{\mu _0}}}{{\pi d}}

answer is D.

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Detailed Solution

Magnetic field at P due to wire 1,  {B_1} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\,(8)}}{d}
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and due to wire 2, {B_2} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\,(6)}}{d}
\Rightarrow B_{net}=\sqrt{B_1^2+B_2^2}=\sqrt{{\left ( \frac{\mu_0}{4\pi}. \frac{16}{d} \right )^2}+\left ( \frac{\mu_0}{4\pi}.\frac{12}{d} \right )^2}
= \frac{{{\mu _0}}}{{4\pi }} \times \frac{2}{d} \times 10 = \frac{{5{\mu _0}}}{{\pi d}}

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Two infinite length wires carry currents 8A and 6A respectively and placed along X and Y-axis. Magnetic field at a point  P(0,0,d)m will be