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(D) The magnetic field $B$ at a distance $r$ from the long straight wire carrying current $I$ is given by $B = \frac{{\mu _0}I}{2\pi r}$.Consider a sm

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None of these

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(D) The magnetic field $B$ at a distance $r$ from the long straight wire carrying current $I$ is given by $B = \frac{{\mu _0}I}{2\pi r}$.Consider a small element of length $dr$ on the vertical wire at a distance $r$ from the horizontal wire. The force $dF$ on this element is $dF = i(dr)B = i(dr)\left( \frac{{\mu _0}I}{2\pi r} \right)$.The total force $F$ is obtained by integrating this expression from $r = x$ to $r = x + l$:$F = \int_{x}^{x+l} \frac{{\mu _0}iI}{2\pi r} dr = \frac{{\mu _0}iI}{2\pi} \int_{x}^{x+l} \frac{dr}{r}$$F = \frac{{\mu _0}iI}{2\pi} [\ln(r)]_{x}^{x+l} = \frac{{\mu _0}iI}{2\pi} \ln \left( \frac{x+l}{x} \right)$.Comparing this with the given options,the correct expression is not listed,therefore the answer is $D$.

The magnetic force between the wires as shown in the figure is:

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