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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.
Solution
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.
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