Question

What will be the resultant magnetic field at origin due to four infinite length wires. If each wire produces magnetic field ${}^{\prime }{B}^{\prime }$ 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 $(B_1,B_2,B_3,B_4)$ at origin due to wires $1,2,3\text{and}4$ are shown in the following figure :

$\because$ Magnetic field due to current carrying infinite wire at $x$ distance = $\frac{{\mu }_0}{4\pi }\frac{2i}{x}$

$B_1=B_2=B_3=B_4=\frac{{\mu }_0}{4\pi }\frac{2i}{x}=B$

Net magnetic field at O –

$B_{net}=\sqrt{(B_1+B_2{)}^2+(B_3+B_4{)}^2}$

$B_{net}=\sqrt{(2B{)}^2+(2B{)}^2}=2\sqrt{2}B$