First slide

Magnetic field due to a straight current carrying wire

Question

What will be the resultant magnetic field at origin due to four infinite length wires if each wire produces magnetic field B at origin?

Moderate

A

4B
B

$\sqrt{2} B$
C

$2 \sqrt{2} B$
D

Zero

Solution

Direction of magnetic field (B₁, B₂, B₃ and B₄) at origin due to wires 1, 2, 3 and 4 are shown in the following figure. $B_{1} = B_{2} = B_{3} = B_{4} = \frac{μ_{0}}{4 π} \cdot \frac{2 i}{x} = B .$
So, net magnetic field at origin O
$B_{net} = \sqrt{{(B_{1} + B_{3})}^{2} + {(B_{2} + B_{4})}^{2}}$
$= \sqrt{{(2 B)}^{2} + {(2 B)}^{2}} = 2 \sqrt{2} B$

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