# Magnetic Force between Parallel Conductors

on . Posted in Electromagnetism

Each wire creates a magnetic field around the wire.  The force between the two wires is related to the current of the wires and the distance between the wires.  Magnetic force between parallel conductors is described by Ampere's law and the Biot-Savart law, which are fundamental principles in electromagnetism.  When two current carrying conductors are placed parallel to each other, they create magnetic fields, and these magnetic fields can exert forces on each other.

### Key Points about magnetic force between parallel conductors

• Direction of Magnetic Fields  -  When electric current flows through a conductor, it generates a magnetic field around it.  The direction of the magnetic field is given by the right-hand rule.  If you wrap your right hand around the conductor with your thumb pointing in the direction of current flow, your fingers will curl in the direction of the magnetic field.
• Ampere's Law  -  Ampere's law relates the magnetic field around a closed loop to the current passing through the loop.
• Force Between Parallel Conductors  -  When two parallel conductors carrying currents are placed near each other, the magnetic field produced by one conductor exerts a force on the other conductor.
• Direction of Force  -  The direction of the magnetic force between the two conductors is determined by the relative directions of the currents.  If the currents flow in the same direction, the conductors will attract each other, and if they flow in opposite directions, they will repel each other.
• Magnitude of Force  -  The magnitude of the force increases with increasing currents, decreasing distance between the conductors, and increasing length of the conductors.
• Magnetic Field Lines  -  Magnetic field lines around the conductors help visualize the direction and strength of the magnetic fields.  These field lines form concentric circles around each conductor, and their density indicates the strength of the magnetic field.

The magnetic force between parallel conductors is a concept in electromagnetism and is the basis for many practical applications, including the operation of transformers, solenoids, and electric motors.  Understanding these principles is crucial for designing and analyzing electrical circuits and devices.

### Magnetic Force between Parallel Conductors formula

$$F_m = \mu_o \; I_1 \; I_2 \;/\; 2 \; \pi \; d$$     (Magnetic Force between Parallel Conductors)

$$\mu_o = F_m \; 2 \; \pi \; d \;/\; I_1 \; I_2$$

$$I_1 = F_m \; 2 \; \pi \; d \;/\; \mu_o \; I_2$$

$$I_2 = F_m \; 2 \; \pi \; d \;/\; \mu_o \; I_1$$

$$d = \mu_o \; I_1 \; I_2 \;/\; 2 \; \pi \; F_m$$

Symbol English Metric
$$F_m$$ = magnetic force $$lbm-ft \;/\; sec^2$$ $$N$$
$$\mu_o$$  (Greek symbol mu) = magnetic constant - $$H \;/\; m$$
$$I_1$$ = wire current (amp) 1 $$I$$ $$C \;/\; s$$
$$I_2$$ = wire current (amp) 2 $$I$$ $$C \;/\; s$$
$$\pi$$ = PI $$3.141 592 653 ...$$
$$d$$ = distance between the wires $$ft$$ $$m$$