Learn about the Force of Two Parallel Current Conductors

Magnetic force is the force of attraction or repulsion which acts between the electrically charged ions because of their motion. This force can be seen in the current-carrying wires, which are parallel to each other and enough in length. The force of attraction or repulsion between the two similar wires is the same whether the current flowing between the wires is the same or different.

The force which acts between the two parallel current-carrying conductors is directly proportional to the current flowing from the conductors and the length of the conductors. The magnitude of this force is contrarily proportional to the space between them or the distance by which the conductors are separated.

Right-Hand Rule for Two Parallel Wires

When a charged particle is in motion in a magnetic field with some speed or velocity, then it will feel a force which is known as the magnetic force. The direction or the angle of this force can be found using the rule of right-hand.

According to this rule, when you point the fingers of the right hand in the direction of the magnetic field, with the velocity of the positively charged particle coming out of your thumb, then the direction of this force on the particle is in the direction where your palm is open.

The magnetic field is generated around the wire when an amount of current is flowing through it. If the length of the wire increases, then the strength of this field decreases as it constitutes the round loops about the wire. Now, for this wire, the direction of the magnetic field for the wire can be found by the right-hand rule of grip.

1. Close the fingers about the wire in which the current is flowing.
2. Close the finger in such a way that the thumb shows the direction of the current flow.
3. Here, the finger will tell the direction of the magnetic loops or field (clockwise or anticlockwise).

Magnetic force on a moving charge

The force on a moving charge which is normal to the speed of the charge and magnetic field, is called the magnetic force. The direction of these parameters is given by the right-hand rule. The magnetic force is able to force the charged particle to travel in a circular or spiral way. When a charged particle passes along the magnetic field line into a region where the field is higher than the force felt by the particle, it reduces the speed of the particle parallel to that area.

What is the force between two parallel wires?

The magnetic field will generate current-carrying wires. When two such wires, in which the current is flowing with some amount, are kept parallel to one another, then the magnetic fields generated in them interact with each other. Magnetic fields result in magnetic force. Hence, the force also interacts with each other.

Now, for the same wire flowing from them, the magnitude of this force is equal, but the direction of the force will be opposite even if the amount of current flowing from them is different.

• In figure , the direction of the flowing current is the same from both the wires. The magnetic field generated in both the wires is opposite in the direction, which can be obtained by the right-hand rule. This opposite-field provides the force of attraction for the two wires

• In figure, the direction of the flowing current is opposite to the first and second wires. The magnetic field generated in both the wires is the same. This results in the force of repulsion in the two wires

How do you find the force between two conductors?

The parallel conductors feel a force when the current is flowing from them, but the question is how much force is flowing between two parallel current-carrying conductors.

The magnitude of the amount of force between two parallel current-carrying conductors is dependent on the following elements.

• The value of current flows from both the conductors
• The total measure of the length of the conductors
• Space between the two conductors

The formula to calculate the force between two conductors per unit length is given below:

FL=oI1I22r

Here, o is the magnetic permeability of the empty space, r is the space between the two conductors I1 and I2 are the current flowing from the conductor 1 and conductor 2 respectively and F/L is the value of force between two conductors per unit length.

Rewrite the formula for the force.

 F=oI1I2L2r 

Here, L is the length of each wire.

Conclusion

A field which is magnetic in nature is obtained around the current-carrying wire or conductor due to the motion of the electric charge. There is a magnetic force produced due to this magnetic field in the wire. 

Similarly, the force of attraction or repulsion between two parallel wires or current-carrying conductors is experienced when the current flows from them. The nature of the force is attractive when the direction of current flow is the same in both wires. The nature of the force is repulsive when the direction of current flow in wires is opposite to each other.