Two parallel wires are separated by a distance $R$ as shown in the diagram. As compared to their separation, the wires are very long, extending well beyond the boundaries of the image. Wire $1$ carries current $I_1.$ Wire $2$ carries current $I_2$ in the opposite direction as the first current. Coordinate axes have been included for convenience.

Part $($a$)$

What is the direction of the magnetic field due to current $I_1$ at the location of Wire $2?$

Part $($b$)$

Enter an expression for the magnitude of the magnetic field due to the current $I_1$ at the location of Wire $2.$

Part $($c$)$

What is the direction of a finite current element $I_2{L}_2$ of the second wire?

Part $($d$)$

Enter an expression for the magnitude of the force on a finite current element $I_2{L}_2$ of Wire $2$ due to the current in Wire $1.$

Part $($e$)$

Enter an expression for the magnitude of the force per unit length on Wire $2$ due to the current in Wire $1.$

Part $($f$)$

What is the direction of the force on Wire $2$ due to the current in Wire $1?$

Part $($g$)$

What is the direction of the magnetic field due to current $I_2$ at the location of Wire $1?$

Part $($h$)$

Enter an expression for the magnitude of the magnetic field due to the current $I_2$ at the location of Wire $1.$

Part $($i$)$

What is the direction of a finite current element $I_1{L}_1$ of the first wire?

Part $($j$)$

Enter an expression for the magnitude of the force on a finite current element $I_1{L}_1$ of Wire $1$ due to the current in Wire $2.$

Part $($k$)$

Enter an expression for the magnitude of the force per unit length on Wire $1$ due to the current in Wire $2.$

Part $(1)$

What is the direction of the force on Wire $1$ due to the current in Wire $2?$

Part $(m)$

Which is the best description of the direction of the forces between two parallel wires with "opposite currents"?

Part $($n$)$

Look carefully at the expressions for the forces on Wire $1$ and Wire $2,$ both magnitude and direction. With hindsight we see that the force on Wire $2$ could be obtained from the expression earlier obtained for Wire $1$ as a direct application of

ANSWER ALL PARTS PLEASE