Question

Two long wires carrying current I₁ and I₂ are arranged as shown in figure. The one carrying current I₁ is along is the x-axis. The other carrying current I₂ is along a line parallel to the y-axis given by x = 0 and z = d. Find the force exerted at O₂ because of the wire along the x-axis.

Answer 1

In this problem first we have to find the direction of magnetic field due to one wire at the point on other wire, then the magnetic force on that current carrying wire.

In Biot-Savart law, magnetic field B is parallel to; dl x r and idl have its direction along the direction of flow of current, or we can find the direction of B with the help of right-hand thumb rule.

We know that force on current (I) carrying conductor placed in magnetic field B is F = I(L × B) = ILB sinθ

The direction of magnetic field at O₂ due to the current I₁ is parallel to Y-axis and in – Y direction.

As wire of current I₂ is parallel to Y-axis, current in I₂ is also along Y-axis. Do I₂ and B1 (magnetic field due to current I₁) are also along Y-axis i.e., angle between I₂ and B₁ is zero. So magnetic force F₂ on wire of current I₂ is F₂ = B₁I₂L₁ sin 0° = 0.