
$(i)\,\,\left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{d\vec l\, \times \,\vec r}}{{{r^3}}}} \right)$
$(ii)\,\, - \left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{d\vec l\, \times \,\vec r}}{{{r^3}}}} \right)$
$(iii)\,\left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{\,\vec r \times d\vec l}}{{{r^3}}}} \right)$
$(iv)\, - \left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{\,\vec r \times d\vec l}}{{{r^3}}}} \right)$

Reason $(R):$ Opposite currents carrying wires repel each other.
$(A)$ If $\vec{B}$ is along $\hat{z}, F \propto(L+R)$
$(B)$ If $\overrightarrow{ B }$ is along $\hat{ x }, F =0$
$(C)$ If $\vec{B}$ is along $\hat{y}, F \propto(L+R)$
$(D)$ If $\overrightarrow{ B }$ is along $\hat{ z }, F =0$