Force b/w two Parallel current carrying wires

Force between two parallel current carrying wires :

To calculate the force between two infinite parallel current carrying wires separated by a distance r , we take an arbitrary point ‘ P ‘ on the second wire, the magnetic field at this point due to other wire is

$ \displaystyle \vec{B} = \frac{\mu_0}{4\pi}\frac{2I_1}{r} (-\hat{k})$

Force on elementary length of the second wire is

$ \displaystyle \vec{dF} = (I_2 dl\hat{j}) \times \frac{\mu_0}{4\pi}\frac{2I_1}{r} (-\hat{k}) $

$ \displaystyle \frac{\vec{dF}}{dl} = \frac{\mu_0}{4\pi}\frac{2 I_1 I_2}{r} (-\hat{i})$

We note that wires carrying current in the same direction attract each other. (Verify using Fleming’s left hand rule).

Also Read:

→ Biot-Savart’s Law
→Magnetic field due to straight conductor carrying current
→ Magnetic field due to Circular Loop
→ Magnetic field at the axis of Circular Loop
→ Solved Examples on Magnetic field due to circular loop
→ Ampere’s Circuital Law & its Applications
→ Magnetic field on the axis of a long solenoid
→ Motion of charged particle in a magnetic field
→ Deviation of charged particle in uniform magnetic field & Cyclotron
→ Force on a current carrying wire in a magnetic field
→Torque on a current carrying loop in a uniform magnetic field
→ Moving coil Galvanometer

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