The current of 5A flows in a square loop of sides 1m is placed in air. The magnetic field at the centre of the loop is . The value of X is ______.

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Solution

Q.
The current of 5A flows in a square loop of sides 1m is placed in air. The magnetic field at the centre of the loop is $X \sqrt{2} \times 10^{- 7} T$ . The value of X is ______. [2024]

Ans.
(40)

i = 5A,

Square of side = 1m

Magnetic field at centre will be into the plane (X), due to all four wires

${\vec{B}}_{net} = 4 B_{1}$

$B_{1} = Magnetic field due to one side,$

$B_{1} = \frac{μ_{0} . i}{4 π r} (\sin θ_{1} + \sin θ_{2}), Here θ_{1} = θ_{2} = 45 °$

$r = \frac{1}{2} m$

$B_{1} = \frac{μ_{0} . (5)}{4 π (1 / 2)} (\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}})$

$B_{net} = 4 B_{1} = 40 \sqrt{2} \times 10^{- 2} tesla$

$∴$ $x = 40$

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