Ncert Exercises & Solutions

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

Hint: The magnetic force will depend on the angle between the magnetic field and the wire.
Step 1: In Biot- Savart law, magnetic field B is parallel to (idl x r) and idl have its direction along the direction of flow of current.

Here, for the direction of the magnetic field at

O_{2}

$O_{2}$ due to the wire carrying the current

I_{1}

$I_{1}$ is:

B is parallel (idl x r) or

\hat{i} x \hat{k}, but \hat{i} x \hat{k} = - \hat{j}

$\hat{i} x \hat{k}, but \hat{i} x \hat{k} = - \hat{j}$

So, the direction of B at

O_{2}

$O_{2}$ is along the y-direction.

Step 2: The direction of the magnetic force exerted at

O_{2}

$O_{2}$ because of the wire along the x-axis;

F = I (l x B) = \hat{j} x (- \hat{j}) = 0

$F = I (l x B) = \hat{j} x (- \hat{j}) = 0$

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

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