Question

What will be the resultant magnetic field at origin due to four infinitely long wires. If each wire produces magnetic field 'B' at origin

• A. $4B$
  
• B. $\sqrt{2}B$
  
• C. $2\sqrt{2}B$
• D. $Zero$

Answer 1

The correct option is C $2\sqrt{2}B$

Direction of magnetic field $(B_1,B_2,B_{3}and{B}_4)$ at origin due to wires 1, 2, 3 and 4 are shown in the following figure.
$B_1=B_2=B_3=B_4=\frac{{\mu }_0}{4\pi }.\frac{2i}{x}=B$. So net magnetic field at origin O
$B_{net}=\sqrt{(B_1+B_3{)}^2+(B_2+B_4{)}^2}=\sqrt{(2B{)}^2+(2B{)}^2}=2\sqrt{2}B$