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  • Two long wires carrying current I_1, and I_2 are arranged as shown in figure. The one carrying current I1 is along the x-axis. The other carrying current I_2 is along a line parallel to the y-axis given by x = 0 and z = d.

Two long wires carrying current I_{1}, and I_{2} are arranged as shown in the figure. The one carrying current I_{1} is along the x-axis. The other carrying current I_{2} is along a line parallel to the y-axis given by x = 0 and z = d. Find the force exerted at O_{2} because of the wire along the x-axis.

Answers (1)

 Firstly, we need to find the direction of the magnetic field caused by one wire on a specific point on the other wire, then determine the magnetic force on the wire carrying current.

According to Biot-Savart law, the magnetic field is parallel to dl x r whereas I dl direction is along the direction of flow of current, but it can also be found out by using the right-hand thumb rule.

Here the direction of the magnetic field at O_{2} , due to the wire carrying I1 current is

\overrightarrow{B}\parallel i\overrightarrow{dl}\times \overrightarrow{r}or \widehat{i}\times \widehat{j}=\widehat{k}

So the direction of  O_{2} is along the Y-direction direction of the magnetic force exerted at  O_{2} because of the wire along the x-axis is

\overrightarrow{F}=\overrightarrow{ll}\times \overrightarrow{B}=\widehat{j}\times (-\widehat{j})=0

So the magnetic field due to the wire is along the y-axis. The second wire is along the y-axis and hence, the force is zero.

 

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