The magnetic force between wires as shown in figure is

Question

The magnetic force between wires as shown in figure is <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/6f92510fe87375960743988b74e5e934-.png" /> (A) (μ0 i I 2/2 π) ℓ n (( x +ℓ/2 x )) (B) (μ0 iI 2/2 π) ℓ n ((2 x +ℓ/2 x )) (C) (μ0 iI /2 π) ln (( x +ℓ/ x )) (D) None of these

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<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/df107fbe699ce91860c053a723462fe4-.png" /> Magnetic field at dr , B =(μ0 I /2 π r ) Force on small element at a distance r of wire of length 1 is dF = i ( dr )((μ0 I /2 π r )) F =(μ0 i I /2 π) ∫ limits x x +ℓ (dr/r)=(μ0 i I /2 π) ℓ n (( x +ℓ/ x ))

Q. The magnetic force between wires as shown in figure is

$\frac{μ _{0} i I ^{2}}{2 π} ℓ n (\frac{x + ℓ}{2 x})$

$\frac{μ _{0} i I ^{2}}{2 π} ℓ n (\frac{2 x + ℓ}{2 x})$

$\frac{μ _{0} i I}{2 π} ln (\frac{x + ℓ}{x})$

None of these

Magnetic field at $d r, B = \frac{μ _{0} I}{2 π r}$
Force on small element at a distance $r$ of wire of length
1 is $d F = i (d r) (\frac{μ _{0} I}{2 π r})$
$F = \frac{μ _{0} i I}{2 π} x \int x + ℓ \frac{d r}{r} = \frac{μ _{0} i I}{2 π} ℓ n (\frac{x + ℓ}{x})$

Q. The magnetic force between wires as shown in figure is

2πμ0​iI2​ℓn(2xx+ℓ​)

2πμ0​iI2​ℓn(2x2x+ℓ​)

2πμ0​iI​ln(xx+ℓ​)

None of these

Magnetic field at dr,B=2πrμ0​I​ Force on small element at a distance r of wire of length 1 is dF=i(dr)(2πrμ0​I​) F=2πμ0​iI​x∫x+ℓ​rdr​=2πμ0​iI​ℓn(xx+ℓ​)

$\frac{μ _{0} i I ^{2}}{2 π} ℓ n (\frac{x + ℓ}{2 x})$

$\frac{μ _{0} i I ^{2}}{2 π} ℓ n (\frac{2 x + ℓ}{2 x})$

$\frac{μ _{0} i I}{2 π} ln (\frac{x + ℓ}{x})$

Magnetic field at $d r, B = \frac{μ _{0} I}{2 π r}$
Force on small element at a distance $r$ of wire of length
1 is $d F = i (d r) (\frac{μ _{0} I}{2 π r})$
$F = \frac{μ _{0} i I}{2 π} x \int x + ℓ \frac{d r}{r} = \frac{μ _{0} i I}{2 π} ℓ n (\frac{x + ℓ}{x})$