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Several forces act between the current-carrying wires since the ordinary currents produce magnetic fields and excrete ample forces on the ordinary current. You might already know that the force between two wires defines Ampere. A magnetic field is due to the Biot – Savart’s law and a current-carrying conductor.
Today, in this article, we will explain one of the most crucial chapters of physics: Force Between Two Parallel Currents – The Ampere. So, if you’re facing difficulties or want to start the preparation process, this article will answer all your popping questions. Without any further ado, let’s get started.
Force Between Two Parallel Currents – The Ampere
- Biot – Savart’s law and the current-carrying conductor contribute to the significance of a magnetic field. Magnetostatics or the Biot- Savart’s Law is another important concept in electricity. It is one of the significant studies of magnetic fields. According to Magnetostatics, the current remains steady or does not change with time. The magnetic line of a current element is-
- We have already studied that an external magnetic field employs a force on a current-carrying conductor and the Lorentz force formula that governs this principle.
- After examining both the studies, it can be concluded that when two current-carrying conductors are positioned parallel, a magnetic force will be excreted.
We have two different current-carrying conductors carrying current I1 and I2, separated d, the distance. As studied in the earlier topics, it can be concluded that due to conductor 1, the conductor carries a similar magnetic field at all points. The magnetic force direction mentioned above is found through the right-hand thumb rule. Because of the first conductor, the magnetic field direction is pointing downwards.
Ampere’s law can be defined as calculating the magnitude of magnetic field lines. As studied till now, the gauss theorem is related to the electric field lines; however, Ampere’s law strictly talks about the magnetic field lines. This magnetic field is associated with the electric current, stating that the electric field never changes as time passes. The relationship between ampere and coulomb is represented as follows:
Ampere = 1 Coulomb / Second
According to Ampere’s circuital law, the magnitude of the field is due to the first conductor. The integral line of magnetic fields, which is written as B near the closed path, is the same as the number of times the algebraic sum of currents passing through the loop. Similarly, the force employed on conductor one by conductor two can be calculated. We already know that the force experienced by conductors one and two is similar except for the directions. Therefore,
F12 = F21
Along with this, we are also aware of the fact that the current flowing in the opposite direction repels the conductor, whereas the current flowing in similar directions attracts the conductor.
Table of Ampere Unit Prefixes
Name | Symbol | Conversion | Example |
microampere(microamps) | μA | 1 μA = 10−6A | I = 40 μA = 40 × 10−6A |
milliampere(milliamps) | mA | 1 mA = 10−3A | I = 2 mA = 2 × 10-3 A |
ampere (amps) | A | – | I = 20 A |
kiloampere(kiloamps) | kA | 1 kA = 103A | I = 4 kA = 4 × 103 A |
How to Calculate the Force Between two Parallel Current-Carrying Conductor
The total force between the two parallel and straight conductors are separated by distance denoted as r, which are calculated as follows.
Consider two parallel current-carrying wires placed parallel to each other and the current passing through these wires are I1 and I2.
Imagine the field excreted by wire 1, and the force exerted on wire 2 is F2. Because of the I1 at the distance r, the magnetic field is B1 = μ0I1/ 2πr. This field is perpendicular and uniform along with the wire 2. Therefore, the force excreted, which is F2, is given by
F = IlBsinθ with sinθ = 1:
When applying Newton’s third law, the forces applied on the wire are the same magnitude. Herefore, we can write F for the F2 Magnitude. Remember, F1 = – F2. As the wires are extremely long, it can be considered force per unit length F/l when B1 is substituted in the last equation. It comes to be F/l = μ0I1I2/2πr.
F/l refers to the force per unit length between the two parallel currents, I1 and I2, further separated by distance. If the current flows in the opposite direction, the force is repulsive, whereas, in the same direction, the force is attractive. This force is vital for the pinch effect in electric plasmas and arcs: no matter whether the current is there or not, the force exits. The definition of ampere is highly determined by forces between current-carrying wires.
Fl=(4 10-7T.mA) (1A)2(2) (1m)=210-7N/m
SinceForces between current-carrying wires highly determine the definition of ampere, μ0 is the same as 4π × 10−7 T⋅m/A, and since 1T = 1N/(A⋅m), the force per meter will be the same as 2 × 10−7N/m.
The total force between the two parallel currents, I1 and I2, is given by F/l = μ0I1I2/2πr.
The SI unit of the electric current is Ampere, donated as A. Also note, that the Ampere’s per second is the unit of charge.
Conclusion
In this article, we studied the Force Between Two Parallel Currents. We also discussed the Ampere Law in detail and other important topics. Reading this information, it will help students to clear their doubts.
We covered the introduction to Force Between Two Parallel Currents – The ampere, the ampere, types Calculated the Force Between two Parallel Current Carrying Conductors, and other related topics. We hope the Force Between Two Parallel Currents – The ampere study material must have helped us understand this topic better.
