Find the force exerted at point 02 because of the wire along the X-axis

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movingcharges

#1

Two long wires carrying currents ${ I }_{ 1 }$ and I2 are arranged as shown in the figure. One carrying current Ix is along the X-axis. The other carrying current I2 is along a line parallel to Y-axis, given by x = 0 and z = d. Find the force exerted at point 02 because of the wire along the X-axis.


#2

Here, first we have to find the direction of magnetic field at point ${{O}{2}}$ due to the wire carrying current
${{I}
{x}}$. Use Maxwell’s right hand grip rule, the direction of magnetic field at point
${{O}{2}}$ due to current /, is along F-axis.
Here, the wire at point ${{O}
{2}}$ Is placed along F-axis. Now, by the formula, F = I2(I x B)
Angle between 1 and B is 0°, both are at Faxis, i.e.
F = ILB sin 0° = 0
So, the force exerted at point ${{O}_{2}}$ because of wire along X-axis is zero.