Four very long wires are arranged as shown in the figure, so that their cross-section forms a square, with connections at the ends so that current I flow through all four wires. The length of each side, of the formed square cross-section, is b . The magnetic field at the central point P (centre of the square) is

Question

Four very long wires are arranged as shown in the figure, so that their cross-section forms a square, with connections at the ends so that current I flow through all four wires. The length of each side, of the formed square cross-section, is b . The magnetic field at the central point P (centre of the square) is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-vhpo20ielqyq1uz5.jpg" /> (A) (μ 0 I/π b) (B) (2 μ 0 I/π b) (C) 0 (D) (μ 0 I/√2 π b)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-vhpo20ielqyqoy2m.jpg" /> net field =2√2 B where B = ((μ )0 I/2 π (. (b √2)2 .)) ∴ net field =(2 μ 0 I/π b)

$\frac{μ _{0} I}{πb}$

$\frac{2 μ _{0} I}{πb}$

$0$

$\frac{μ _{0} I}{2 πb}$

net field $= 22 B$
where $B = \frac{( μ ) _{0} I}{2 π ( \frac{b 2}{2} )}$
$∴$ net field $= \frac{2 μ _{0} I}{πb}$

πbμ0​I​

πb2μ0​I​

0

2​πbμ0​I​

net field =22​B where B=2π(2b2​​)(μ)0​I​ ∴ net field =πb2μ0​I​

$\frac{μ _{0} I}{πb}$

$\frac{2 μ _{0} I}{πb}$

$0$

$\frac{μ _{0} I}{2 πb}$

net field $= 22 B$
where $B = \frac{( μ ) _{0} I}{2 π ( \frac{b 2}{2} )}$
$∴$ net field $= \frac{2 μ _{0} I}{πb}$