A rectangular loop of wire of size $4 c m \times 10 c m$ carries steady current of 2 A. A straight long wire carrying 5 A current is kept near the loop as shown. If the loop and the wire are coplanar, find the magnetic flux through the rectangular loop.

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Solution

Given,

$I = 3 A$

$s = 1 c m$

$w = 4 c m$

$l = 10 c m$

$μ_{0} = 4 π \times 10^{- 7} N / m^{2}$

The magnetic flux though the rectangular loop,

$ϕ_{B} = \frac{μ_{0} I l}{2 π} l n (\frac{s + w}{s})$

$ϕ_{B} = \frac{4 π \times 10^{- 7} \times 3 \times 10 \times 10^{- 2}}{2 π} l n (\frac{1 + 4}{1})$

$ϕ_{B} = 9.6 \times 10^{- 8} W b$

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