How Does Electric Current Create a Magnetic Field?
With the help of magnetic field lines, we can visualise the magnetic field. Faraday introduced the concept of the magnetic field lines. The magnetic field lines give us the pattern of the magnetic field. Using iron filings or a magnetic compass, we can find the shape of the magnetic field.
In this article, we will have a deep insight into the magnetic field produced by a current carrying conductor and Maxwell’s right hand thumb rule to find the direction of the magnetic field.
History of Inventor
Hans Christian Oersted
Magnetism has been known since ancient times. In 1820, Hans Christian Oersted invented a very useful phenomenon. He was born in Rudkobing, Denmark. He observed that when the electric wire carries electric current, it behaves like a magnet. He established the relation between electricity and magnetism in the 19th Century.
What is Magnetic Field?
The region surrounding the magnet in which the force of the magnet can be felt is called the extent of the magnetic field. Its SI unit is Tesla and it is named after the American Scientist Nikola Tesla. Gauss is the smaller unit of the magnetic field.
Properties of Magnetic Field Lines
The list of properties of magnetic field lines of a bar magnet is as follows:
Magnetic Field Lines
Magnetic field lines generally originate from the North Pole of the magnet and end at the South Pole but inside the magnet, the magnetic field lines are directed from the South Pole to the North Pole. Thus, we can say that they are closed curves.
These field lines can never intersect each other because at the point of intersection, we get two directions of magnetic field which is not possible.
The magnetic field is strong where field lines are crowded and vice-versa.
Magnetic Field Due to a Current in Straight Conductor
Consider the circuit shown here. Here, the conductor is connected to a simple circuit consisting of a variable resistance, an ammeter and a battery. The top end of the conductor is connected to the positive end of the battery. The other end of the conductor is connected to the negative side of the battery. The conductor is passed through a small sheet of cardboard and we have sprinkled some iron filings on the cardboard around the conductor.
As soon as we turn on the battery, the current starts flowing. As soon as the current starts flowing, we see that the iron filings which were randomly arranged around the conductor start arranging themselves in a specific pattern and the specific pattern is concentric circles which we have shown in the figure given below. All these concentric circles have just one centre which is nothing but the conductor itself and from the centre, the magnetic field originates in the form of concentric circles.
Magnetic Field
We can find out the direction of the magnetic field with the help of Maxwell’s right hand thumb rule. This rule says that if you point the thumb in the direction of the current, then the direction in which your fingers curl the conductor will give you the direction of the magnetic field.
So, in order to apply the right hand thumb rule, hold a straight conductor in your right hand such that your thumb points the direction of current of this straight conductor, then the direction in which fingers are wrapped around this straight conductor is the direction of the magnetic field. This is shown in the below figure. This we can understand with the help of the figure given below.
If the conductor is carrying current in an upward direction, then the direction of the magnetic field will always be in an anticlockwise direction. But if the conductor is carrying current in a downward direction, then the direction of the magnetic field will be in a clockwise direction.
Direction of Magnetic Field
If the direction of current is changed, the direction of magnetic field lines also changes which we can see in the above figure.
The magnitude of magnetic field produced by this straight current carrying conductor at a given point is
Directly proportional to the current passing through this straight conductor. That means, $B$ is proportional to $I$
Inversly proportional to its distance $r$ from this current carrying straight conductor. That means, $B$ is inversely proportional to $\dfrac{1}{r}$.
So, magnetic field due to straight current carrying conductor (infinitely long) is given by
$B = \dfrac{{{\mu _0}I}}{{2\pi r}}$
Where, ${\mu _0} = 4\pi \times {10^{ - 7}}Tm{A^{ - 1}}$ and it is the permeability of free space, $I$ is the current flowing in the long straight conductor and $r$ is the distance of the magnetic field from that straight conductor.
Interesting Facts
Magnetite is the most magnetic natural metal on the Earth.
The magnetic field of the Earth is 1000 times weaker than the bar magnet.
We can not separate the North Pole and the South Pole of a magnet.
Conclusion
From the above discussion, we can conclude that the magnetic field lines around a current carrying straight conductor are concentric circles whose centres lie on the conductor. Moreover, if the direction of the current in a straight conductor is known, then with the help of Maxwell's right hand thumb rule, we can find the direction of the magnetic field produced by it.
FAQs on Magnetic Field Due to a Current Through a Straight Conductor
1. What happens when an electric current flows through a straight conductor?
When an electric current flows through a straight conductor, it generates a magnetic field in the space surrounding the wire. This phenomenon, first observed by Hans Christian Oersted, demonstrates the direct relationship between electricity and magnetism. The magnetic field lines form concentric circles in a plane perpendicular to the conductor, with the conductor at the centre of these circles.
2. How can you determine the direction of the magnetic field around a straight current-carrying conductor?
The direction of the magnetic field can be easily determined using the Right-Hand Thumb Rule. To apply this rule, imagine holding the current-carrying straight conductor in your right hand such that your thumb points in the direction of the current flow. The direction in which your fingers curl around the conductor gives the direction of the magnetic field lines.
3. What are the key factors that affect the strength of the magnetic field produced by a straight conductor?
The strength of the magnetic field (B) around a long, straight conductor is influenced by two main factors:
- Magnitude of the Current (I): The field strength is directly proportional to the amount of current flowing through the conductor. A stronger current produces a stronger magnetic field.
- Distance from the Conductor (r): The field strength is inversely proportional to the perpendicular distance from the conductor. The field is strongest near the wire and weakens as you move away from it.
4. Why do the magnetic field lines form concentric circles around a straight conductor?
The circular shape of the magnetic field lines is a direct consequence of the physical symmetry of the setup. For a long, straight wire, every point at the same perpendicular distance (r) is identical. According to the laws of electromagnetism (like the Biot-Savart Law), there is no reason for the magnetic field to be stronger or weaker at any particular point on a circle drawn around the wire. This symmetry results in the magnetic field having a constant magnitude at a fixed distance, forming perfect concentric circles.
5. What is the formula for calculating the magnetic field of a long, straight current-carrying wire?
For a very long (or infinitely long) straight conductor, the magnitude of the magnetic field (B) at a perpendicular distance (r) from the wire can be calculated using Ampere's Law. The formula is:
B = (μ₀I) / (2πr)
Where:
- B is the magnetic field strength.
- μ₀ is the permeability of free space (a constant, 4π × 10⁻⁷ T·m/A).
- I is the current in the conductor.
- r is the perpendicular distance from the conductor.
6. How does the magnetic field pattern of a straight conductor differ from that of a circular loop?
The magnetic field patterns are significantly different:
- Straight Conductor: Produces a magnetic field with concentric circular field lines centred on the wire. The field strength decreases as the distance from the wire increases.
- Circular Loop: Produces field lines that are circular near the wire but become nearly straight and parallel as they pass through the centre of the loop. The magnetic field is strongest and most uniform at the centre of the loop.
7. What are some practical applications of the magnetic field produced by a straight conductor?
While often demonstrated as a basic principle, the magnetic field from a straight conductor is fundamental to many technologies. For example, the effect is crucial in understanding the magnetic interference from power transmission lines, the basic operating principle of simple electromagnets, and forms the conceptual basis for designing more complex components like coils and solenoids used in motors, generators, and transformers.
8. Is there a magnetic field inside the straight conductor itself, or only outside it?
Yes, a magnetic field also exists inside the conductor. Assuming the current is distributed uniformly across the conductor's cross-section, the magnetic field inside starts at zero at the very centre and increases linearly with the distance from the centre, reaching its maximum value at the surface of the conductor. Outside the conductor, the field begins to decrease inversely with distance, as described by the standard formula.
9. How is the magnetic field of a straight wire different from the uniform field inside a solenoid?
The primary difference lies in the uniformity and shape of the field:
- Straight Wire: The magnetic field is non-uniform (it weakens with distance) and its field lines are circular, wrapping around the wire.
- Long Solenoid: The magnetic field inside a long solenoid is almost perfectly uniform and strong, with straight, parallel field lines running along the axis of the solenoid. The external field of a solenoid is very weak, similar to that of a bar magnet.
