Magnetic Field And Current: 9 Facts You Should Know

The magnetic field and current are considered to be two faces of the same coin because of the involvement of charges, and both are derived from electromagnetic radiation or field.

An electromagnetic wave is of both electric and magnetic fields. The current is due to the electric field. Thus there will be a close relationship between the magnetic field and current. This post is concerned with an exhaustive explanation and facts related to the magnetic field and current and their relation to the electromagnetic field.

Relation between magnetic field and current

An electric current in a wire creates a magnetic field due to the motion of the charges. This leads to explaining the relationship between the magnetic field and current, which is explained by the Biot-Savart law. It states that “a current I flowing in a current-carrying conductor of small length dl is nothing but the elementary source of the magnetic field.

If you consider a wire carrying current I along the length dl in the wire, then the magnetic field due to the current at a point of observation with respect to the wire is given as,

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Where; μ0 is the permeability of the frère space(4π×10-7N/A2), and R is the distance between the point and wire.

Integration of the above equation gives the magnetic field due to the current flowing through the wire loop. The magnetic field and current are interdependent on each other. As the rate of current flow rises, the strength of the magnetic field will be greater due to the motion of the conductive charges.

How does magnetic field effect current?

When a current-carrying wire is made to be in contact with changing magnetic field, a current is induced in the wire. This current flows due to the magnetic field lines applying some force on the charges causing them to move.

Since magnetic field and current are closely related, a small change in the magnetic field produces electromotive force in the wire. It happens because the changing magnetic field generates the electric field, and charges are set free to flow, and thus current is induced.

The magnetic field is associated with the current flow direction. If the direction of the magnetic field changes, the current flow inside the conductor also changes.

Direction of magnetic field and current

The direction of orientation of magnetic field and current are normal to one another. Since we know that, in an electromagnetic wave, the motion of electric field and magnetic field are always in perpendicular directions. The current is nothing but a form of electrical energy carrying the free electron flow.

Generally, the right-hand rule give an account to describe the direction of both magnetic field and current. First, make an L-shape hand gesture using the thumb and the index finger, then point the middle finger perpendicular to both the fingers. The remaining fingers are kept curled. This type of right-hand gesture helps to remember the direction of the magnetic field and current.

The magnetic field offers some force exerted on the moving charges. When the charges are at rest, the magnetic field does not influence the charge. But as soon as they begin to move, the force created by the field pushes the charges, and current flows across the wire. The direction of current flow is not in the direction of the field lines but instead traces a perpendicular path.

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Right hand rule to show direction of magnetic field and current
Image credits: Wikimedia commons

According to the rule, your hand resembles a current-carrying wire, and the direction of the positive charge is indicated by your pointer. And magnetic field is indicated by your middle finger, and your thumb indicates the motion of the current due to the magnetic force.

Why is magnetic field perpendicular to current?

The magnetic force exerted on the charges is always a cross-product of the velocity of the charges to conduct current and magnetic field. The cross product of any two vector quantity is always exerted right angle to the applied force. Thus, the magnetic field is perpendicular to the current.

The magnetic force is considered as the Lorentz force that is exerted on the charges and makes them move and causes them to conduct current. Since the magnetic field is a vector quantity and the velocity of the charges contributes to the flow of current is also a vector quantity. The cross product of these two vector quantities must be a perpendicular force. Thus, the magnetic field and current are perpendicular to each other.

Is magnetic field always perpendicular to current?

Yes, since the electric field is always oriented perpendicular to the magnetic field in EM wave, the current is due to the electric field. Thus magnetic field and current are also perpendicular.

Consider a wire-carrying current, and magnetic field B is generated when there is the flow of current in the wire. The arrow-headed straight line in the middle indicates the direction of the current in the wire, and the circular ring around the current is the magnetic field whose direction is indicated using an arrow.

How is the magnetic field perpendicular to the current?

Generally, the current carries the moving charges across the wire resulting in the generation of the magnetic field, which is curled around the wire in the form of a ring. The perpendicular orientation of the magnetic field and current is due to this curling phenomenon illustrated as the second right-hand rule.

According to this rule, if you curl all your fingers across the palm and the thumb heading upward, illustrate how the magnetic field is perpendicular to the current. The direction of the curl is perpendicular to the current flow indicated by the thumb pointed up.

If the current flows from an upward to a downward direction, the magnetic field will be clockwise perpendicular to the exerted force. And if the current is moving from downward to upward, the magnetic field is orientated in an anti-clockwise orientation.

When magnetic field is perpendicular to current?

When the force exerted on the charges is maximum, the charges begin to move normally in the direction of the field lines. Due to the motion of the charges, the resultant current tends to follow the same way perpendicular to the magnetic field.

The interaction of force with the magnetic field is quite different. If there are no force means, there will be no motion of the charges and no magnetic field. If the magnetic field is parallel to the current, it is quite impossible to establish a relationship between them.

What is the relationship between the direction of current flow and magnetic polarity?

The direction of current and magnetic polarity is correlated. If the direction of the magnetic field is from north to south pole, the flow of charges in the current-carrying conductor takes place from negative to positive charges.

This means that, if the direction of the current changes, then the direction of the magnetic field lines also charges. Suppose, initially, the current flows from negative to positive, and the magnetic field lines emerge from the north to the south pole. By reversing the direction of the current flow, we can observe that the magnetic field lines also reverse its direction from south to north pole.

The left-hand rule is usually helpful in demonstrating the effect on magnetic polarity due to the direction of the current. In this rule, the thumb indicates the direction of the north pole when electrons flow from the negative to the positive terminal.

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Orientation of magnetic field and current
Image credits: Wikimedia commons

How does a magnetic field affect current in a magnetic circuit?

The magnetic fields in the magnetic circuit drive the magneto-motive force, similar to the electromotive force driven by the electric field. The magneto-motive force from the magnetic field depends on the coil turns and current.

A magnetic circuit consists of a coil made of closed-loop magnetic flux. If we increase the number of turns in the coil, the magnetic field strength increases proportionately, causing increasing the flux. The flux induces more current to establish maximum magneto-motive force.

The magnetic circuits are analogous to an electric circuit. But the difference is in an electric circuit, the motion of the charges causes a magnetic field, and in a magnetic circuit, the magnetic field induces the current in the circuit.

Magnetic field and current graph

Since the magnetic field and current are correlated to each other, the plot of the magnetic field and current varies linearly with each other. The graph of magnetic field vs. current gives a straight line increasing linearly with each other.

The linear increase of magnetic field is due to as the current in the wire loop increases, the motion of the charges also increases which causes to generate of the more magnetic field in the loop.

magnetic field and current
Magnetic field and current graph

The slope of the graph gives a physical constant that represents the number of winding of the wire loop.

Solved problems on the magnetic field and current

Calculate the magnetic field due to the current-carrying wire of unit length carrying 5amp of current through it at a distance of 3m.

Solution:

Given –the current in the wire, I= 5amps

The distance between the wire r= 3m

The magnetic field B at the point r is

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The value of μ0 is 4π×10-7 N/A2; substituting the values in the above equation, we get

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B=3.33×10-7T.

Two current-carrying wire of the same length is placed parallel to each other, separated from a distance of 2m. One wire carries the current of 12amps, and the other carries the current of 15amps. Calculate the magnetic field arising from both parallel wires at a distance of 5m.

Solution:

Given –the current carried by one wire I1=12amps

The wire carried by another wire I2=15 amps

The distance r1=5m.

The distance r2=7m.

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Free-hand diagram of two parallel wire

The permeability of the free space μ0=4π×10-7 N/A2

The magnetic field due to both wires is given by

B=B1+B2

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B=4.8+4.28

B=9.085×10-7T

Calculate the magnetic field at a point of a distance of 8m from the wire carrying a current of 14amps.

Solution:

Given –the point at a distance away from the wire r=8m

The wire carrying the current I=14amps.

The permeability of free space μ0=4π×10-7 N/A2

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Substituting the given values in the above equation

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B=3.5×10-7T.

Conclusion

From this post, we understand the relation between the magnetic field and current and we learnt magnetic field and current are the vector quantity oriented normal to plane of electromagnetic wave. The behavior of charges in magnetic field yields current. The fast motion of the charges in a current carrying wire is responsible for magnetic field. this is how magnetic field and current are related.

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