Two infinite length wires carries currents 8A and 6A respectively and placed alo

Question

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

Options:

A . 7μ0πd

B . 10μ0πd

C . 14μ0πd

D . 5μ0πd

Answer: Option D
:
D
Magnetic field due to P due to wire 1,

B_{1} = \frac{μ_{0}}{4 π} . \frac{2 (8)}{d}

and due to wire 2,

B_{2} = \frac{μ_{0}}{4 π} . \frac{2 (6)}{d}

\Rightarrow B_{n e t} = \sqrt{B_{1}^{2} + B_{2}^{2}}

= \sqrt{{(\frac{μ_{0}}{4 π} . \frac{16}{d})}^{2} + {(\frac{μ_{0}}{4 π} . \frac{12}{d})}^{2}}

= \frac{μ_{0}}{4 π} \times \frac{2}{d} \times 10 = \frac{5 μ_{0}}{π d}

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