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

• A. $\frac{7{\mu }_0}{\pi d}$
  
• B. $\frac{10{\mu }_0}{\pi d}$
  
• C. $\frac{14{\mu }_0}{\pi d}$
  
• D. $\frac{5{\mu }_0}{\pi d}$
  

Answer 1

The correct option is D $\frac{5{\mu }_0}{\pi d}$


Magnetic field at P due to wire 1, $B_1=\frac{{\mu }_0}{4\pi }.\frac{2\left(8\right)}{d}$



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