Force Between Parallel Current Carrying Wires
Consider two long wires `1` and `2` kept parallel to each other at a distance `r` and carrying currents `i_1` and `i_2` respectjvely in the same direction.
Magnetic field on wire 2 due to current in 1 is given by Biot Savart's law as
`B = (mu_0i_1)/(2pir)` [in `otimes` direction]
Magnetic force on a small element `dl` of wire `2` due to this magnetic field is,
`dvecF = i_2(dvecl xx vecB)`
Magnitude of this force is, `dvecF = i_2[(dl)(B) sin90^0]`
= `i_2 (dl)((mu_0i_1)/(2pir)) = mu_0/(2pi) .(i_1i_2)/r dl`
Direction of this force is along `dvecl xx vecB` or towards the wire 1.
The force per unit length on wire 2 due to wire 1 is,
`(dF)/(dl) = mu_0/(2pi). (i_1i_2)/r` ...................................(1)
The same force acts on wire 1 due to wire 2. The wires attract each other if the current in the wires are flowing in the same direction and they repel each other if the currents are in the opposite direction. The force of attraction or repulsion between two current carrying wires is often called Ampere Force.
Magnetic field on wire 2 due to current in 1 is given by Biot Savart's law as
`B = (mu_0i_1)/(2pir)` [in `otimes` direction]
Magnetic force on a small element `dl` of wire `2` due to this magnetic field is,
`dvecF = i_2(dvecl xx vecB)`
Magnitude of this force is, `dvecF = i_2[(dl)(B) sin90^0]`
= `i_2 (dl)((mu_0i_1)/(2pir)) = mu_0/(2pi) .(i_1i_2)/r dl`
Direction of this force is along `dvecl xx vecB` or towards the wire 1.
The force per unit length on wire 2 due to wire 1 is,
`(dF)/(dl) = mu_0/(2pi). (i_1i_2)/r` ...................................(1)
The same force acts on wire 1 due to wire 2. The wires attract each other if the current in the wires are flowing in the same direction and they repel each other if the currents are in the opposite direction. The force of attraction or repulsion between two current carrying wires is often called Ampere Force.