Magnetic Flux In A Wire: 7 Facts You Should Know

A number of magnetic field lines that pass through a given area are called magnetic flux. The magnetic flux helps to predict the direction and effect of the magnetic field in the given area.

Magnetic fields are the basic reason for magnetic flux to arise. It describes the field interaction at each point associated with the moving charges at that region. Since wire carries the charges, let us discuss briefly the facts associated with magnetic flux in a wire in this post.

Is there a magnetic flux in a wire?

In a current-carrying wire, there is magnetic flux. The moving charges always contribute to the generation of the magnetic field. This magnetic field induces the magnetic flux in the wire.

Since we know that a wire can generate an electric field even if there is no motion of the charges. Similarly, a wire can generate magnetic flux only when a motion of charges occurs. The moving charges generate the magnetic field in a wire. If we consider a wire loop, the magnetic field lines pass through the loop creating the flux.

Suppose a uniform magnetic field is generated in a wire of unit length carrying the current perpendicular to the field. In that case, it experiences a normal force in the direction perpendicular to both the magnetic field and current. This creates magnetic flux in the wire.

What is the magnetic flux in a wire?

The total number of magnetic field lines penetrating from the given wire area is called magnetic flux in a wire. The magnetic flux in a wire also describes the effect of magnetic force evolved in the wire.

If we consider a wire which consists of moving charges, the magnetic field is generated. The magnetic field lines in the wire always have a direction; the direction in which the magnetic field lines pass inside the wire is usually represented by magnetic flux. Magnetic flux is a vector quantity as it has both magnitudes as well as direction.

Magnetic flux is the imaginary line which visualizes the strength of the magnetic field generated in the wire and the direction of propagation of the field lines. The SI unit of magnetic flux is Weber(Wb), indicated by the letter φB, where B represents the magnetic field.

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Magnetic flux in a wire
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What is the magnetic flux density in a wire?

The normal reaction force exerted per unit length of a given wire per unit current where the magnetic field is at the right angle to the current flow is called magnetic flux density. The unit of magnetic flux density is Tesla, denoted by the letter B.

The magnetic flux density simply measures the strength of the magnetic field in the wire. The magnetic flux density describes the number of field lines that can exist in a wire carrying current perpendicular to the field. The magnetic flux density is also a vector quantity.

Since wire carries the current, the magnetic flux density is highly influenced by the electric field, similar to the electric current influenced by the other electric field. The formula to find the magnetic flux density in the wire is given below.

B=F/Il Where F is the perpendicular force, I is the current, and l is the wire length.

The surrounding medium of the wire also influences the flux density. The magnitude of flux density depends on the two factors,

  • Strength of the current
  • The perpendicular distance from the point of the wire

We know that B is highly dependent on the length of the wire, but the radius of the wire cannot be negligible even if it is very small. So the magnetic flux density for a long straight wire is given by

gif

Where μ is the permeability of the medium. In a vacuum, the permeability is 4π×10-7Hm-1.

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Magnetic flux
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How to find the magnetic flux of a wire?

The magnetic flux penetrating through the wire is calculated by using the magnetic field evolved in the wire and the area of cross-section of the wire. The product of area and magnetic field simply gives the magnetic flux.

φB=B A

The magnetic flux generated is always perpendicular to the magnetic field. Thus it makes an angle between the normal and magnetic field. Considering this fact, the magnetic flux is given by

φB=B.A cosθ

Where θ is the angle between the normal and magnetic fields.

The steps given below must be followed to find the magnetic flux in a wire.

  • Identify the given values of the magnetic field, area and angle. If the area of the wire is not mentioned explicitly, calculate the area using the dimensions of the given wire (using length, thickness, radius etc.)
  • Do not use the same angle in the calculation if the angle is given. Subtract the given angle by 90° and then use the obtained angle for the calculation.
  • The magnetic field must be expressed in Tesla, and the area must be in m2.
  • Then put the values in the equation, calculate the φB and express the obtained value by Wb.
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Magnetic flux in a wire
Image credits: Wikimedia commons

What are the factors that affecting magnetic flux in a wire?

There are four factors that affect the magnetic flux in a wire; they are

  • Strength of the magnetic field B
  • The area of the cross-section of the wire
  • The angle between the normal to the surface and magnetic field in the wire
  • The flow of current in the wire

A small change in the factor, as mentioned earlier, affects the magnetic flux in the wire. The magnetic field strength is correlated to the magnetic flux in a wire if the magnetic field generated in a wire is strong, the magnetic flux in a wire increases. The area of the wire also directly corresponds to the magnetic flux. The larger the area of the wire, the more flux can penetrate through the wire.

The magnetic field must be perpendicular to the surface so that magnetic flux can be penetrated at the right angle to each other. Current is directly related to magnetic force. As the flow of current increases, the magnetic force increases by increasing the strength of the field; thus, flux is also increased.

Varying any of the factors mentioned above leads to a change in magnetic flux. The magnetic flux change induces the electromotive force in the wire.

What happens to the magnetic flux if we replace a wire with a bunch of wires?

The strength of the magnetic flux increases with the bunch of wires. Since magnetic flux is due to the magnetic field evolving in the wire due to the motion of the charges, as a bunch of wires replaces a single wire, the magnetic field strength increases, increasing the flux.

The magnetic field follows the superposition principle: “the magnetic field acting on a point due to multiple sources is equal to the vector sum of all the individual magnetic fields at that point.” This eventually explains that if we consider a point where multiple wires are used to generate magnetic fields, each individual wire contributes a certain magnetic field to give a strong field.

The magnetic flux penetrated from a bunch of wires is also due to the magnetic field contributed by each wire. So the magnetic flux from the bunch of wire is more. The formula gives the magnetic flux due to a bunch of wires

φB=n B.A cosθ; Where, n represents the number of wires employed to generate flux.

Solved Problems with magnetic flux in a wire

Calculate the magnetic flux in a wire in which a uniform magnetic field of 4.2T is acting perpendicular to the surface of the wire of an area of 0.08m2.

Solution:

Given –the strength of the magnetic field, B=4.2T

Area of the cross-section of the wire A=0.08m2

Since the angle between the surface and magnetic field is not mentioned, we can neglect the angle. The formula gives the magnetic flux

φB=B.A

φB=(4.2)(0.08)

φB=0.336Wb.

A wire of area 0.0078m2 generates a magnetic field of 3.33T at an angle of 35° perpendicular to the wire loop. Calculate the magnetic flux generated through that wire.

Solution:

Given –magnetic field B=3.33T.

Area of the wire A=0.0078m2

Angle normal to the magnetic field =35°.

The angle can be found as θ=90°-(measured angle)

θ=90°-35°

θ=55°

The magnetic flux is

φB=B.A cosθ

φB=(3.33)(0.0078)cos(55)

φB=(0.0259)(0.573)

φB=0.01488Wb

Conclusion

From this post, we get to know that magnetic flux in a wire is a vector quantity which describes the effect of magnetic force generated in the wire. The magnetic flux is due to the magnetic field strength, which follows the superposition principle.

Read more about Is Magnetic Flux A Vector?

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