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The force of attraction or repulsion between two parallel current-carrying conductors is often called Ampere's force law.
- The origin of this force is due to the existence of a magnetic field caused by a current-carrying conductor and Biot – Savart's law.
- An external magnetic field generally exerts a force on a current-carrying conductor and the Lorentz force is the formula that governs this principle.
- As a result of the two studies, we can conclude that any two current-carrying conductors placed near each other will exert a magnetic force on each other.
- If the currents in parallel wires are in opposite directions, the wires repel each other and if the current in the wires is flowing in the same direction, the wires will attract each other.
| Table of Content |
Key Terms: Parallel current-carrying conductors, Force, Conductors, Fleming's left-hand rule, Ampere, Biot-Savart law, Current, Magnetic field
Also Check: Moving Charges and Magnetism
Force between Two Parallel Current Carrying Conductors
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The forces between two wires are to be used to define an ampere and this force explains why large circuit breakers burn up when attempting to interrupt large currents.
Consider two infinitely long parallel conductors X and Y carrying currents I1 and I2 respectively in the same direction. The magnetic force at any point on conductor Y due to current I1 in the conductor X is given by
\(B_1={\mu_0 \over 4\pi}({2I_1 \over d})\) …….. (i)
The direction of B1 with reference to conductor Y is perpendicular to the plane of the conductor and is vertically downward.
We know, a current-carrying conductor of length L placed at the right angle to the magnetic field B experience a force, which is given by
F = BIL
Therefore force experienced per unit length of conductor Y in the magnetic field B1 is given by
F = B1I2 x 1 = B1I2
Using equation (i),
\(F_2={\mu_0 \over 4\pi}({2I_1 \over d})I_2={\mu_0 \over 4\pi}({2I_1I_2 \over d})\)
Using Fleming's left-hand rule, the direction of F2 is in the plane of the conductor directed towards conductor X.
Similarly,
\(F_1={\mu_0 \over 4\pi}({2I_1I_2 \over d})\)
F1 is in the plane of the conductor and directed towards conductor Y.
Since F1 and F2 are equal and opposite, so these forces pull the two conductors towards each other.
Hence, we conclude that:
- Two long parallel conductors carrying currents in the same direction attract each other.
- Two long parallel conductors carrying currents in opposite directions repel each other.
Also Read:
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| Magnetic force on a current-carrying conductor | Magnetic Field on the axis of a circular current loop | Potential Energy |
Definition of Ampere
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In general, the force between two current-carrying parallel conductors is given by
\(F={\mu_0 \over 4\pi}({2I_1I_2 \over d})\)
If I1 = I2 = 1 ampere and d = 1 meter, then
\(F={4\pi \times 10^{-7}\over 4\pi}({2\times 1 \times 1 \over 1})=2 \times 10^{-7} N\)
Ampere is that current which if maintained in two infinitely long parallel conductors of negligible cross-sectional area separated by 1m in vacuum cause a force of 2 x 10-7 N on each meter of the wire.
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Things to Remember
- The forces between two wires are to be used to define an ampere and this force explains why large circuit breakers burn up when attempting to interrupt large currents.
- Ampere is that current which if maintained in two infinitely long parallel conductors of negligible cross-sectional area separated by 1m in vacuum cause a force of 2 x 10-7 N on each meter of the wire.
- Two long parallel conductors carrying currents in the same direction attract each other.
- Two long parallel conductors carrying currents in opposite directions repel each other.
Sample Questions
Ques: What exactly do you mean by "current-carrying conductor"? (2 marks)
Ans: As we have already seen, it is carrying a direct current (DC), which means that some flux lines will be generated around the conductor, and they are concentric with the conductor's central axis. So we can say that an electromagnetic field is formed as a result of this current flowing through this conductor.
Ques: Explain why two parallel current-carrying conductors attract. (2 marks)
Ans: If we have two current-carrying wires that are said to be parallel wires with magnetic fields circling them in the same direction, they will attract each other at the point where their respective magnetic fields intersect.
Ques: Why Do Parallel Currents Attract Each Other? (2 marks)
Ans: When the currents flow in the same direction, the magnetic field is opposite and the wires attract. So, if electrons are present in both wires that are said to be moving in the same direction, they see the same number of electrons in the other wire because they are moving at the same speed.
Ques: How can an Electric field be shielded by the Faraday cage effect? (5 marks)
Ans: Consider the system depicted in the diagram above. Here we can see that we have two parallel current-carrying conductors separated by a distance denoted by 'd.' We can also see that conductor 2 experiences the same magnetic field as conductor 1 at every point along its length. That is, the magnetic force direction is indicated in the figure and is determined using the right-hand thumb rule. The magnetic field's downward direction is a result of the first conductor. According to Ampere's law of circuits, the magnitude of the field due to the first conductor can be calculated as follows:
Ba=μ0I1/2πd
The force exerted by conductor 1 on a segment of length denoted by the letter L of conductor 2 can be expressed as follows:
F21=I2LB1=(μ0I1I2/2πd)L
Similarly, we can calculate the force exerted by the conductor, which is the number 2, on conductor 1. As a result, we can see that conductor 1 experiences the same force as conductor 2 but in the opposite direction. As a result, we can write it down as follows:
F12 = F21
Ques: How can the magnetic force of 50 C charge particles traveling at 3m/s in a 1T magnetic field be calculated? Its field is pointing in the same direction as the path of the second particle. (2 marks)
Ans: Given parameters : q=50C, v=3m/s, and B=1T
Because the path difference of the second particle is the same as the direction of its field, θ=0°
F= q v B sin θ = 50x3x1x sin θ =0 is the magnitude force formula.
Ques: What are magnetic flux lines what is the significance of magnetic flux? (3 marks)
Ans: Magnetic flux lines are significant for a number of reasons:
Magnetic field lines are lines in a magnetic field whose tangent determines the field direction at any given point and whose density determines the field magnitude. They show the path of the magnetic field.
The strength of the magnetic field is determined by the number of magnetic field lines. The magnetic field is stronger at the poles because the lines are longer. A magnetic field's strength is proportional to the number of magnetic field lines present in a given area.
Ques: What is Fleming’s right-hand rule? (4 marks)
Ans: When a conductor connected to a circuit moves in a magnetic field, Fleming's right-hand rule (for generators) shows the direction of the induced current. It can be used to determine the current direction in a generator's windings.
The thumb, index finger, and middle finger of the right hand are held perpendicular to each other (at right angles).
- The thumb is pointing in the direction of the conductor's motion relative to the magnetic field.
- The first finger is pointing toward the magnetic field. It is, by convention, the direction from the North to the South magnetic pole.
- The direction of the induced or generated current within the conductor is then represented by the second finger.
Ques: Explain the Magnetic force on a current-carrying conductor. (2 marks)
Ans: If there is a conductor carrying current, the charges are moving and each charge experiences a force as a result of the motion. The charges on particles and those particles form the conductor, allow us to feel a force on the conductor in this manner. And the magnetic force acting on both the charge and the conductor is referred to as the Current Carrying Conductor.
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