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Magnetic Force on a Current Carrying Wire. Ampere's Force Revision Notes

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16.3Magnetic Force on a Current Carrying Wire. Ampere's Force


In these revision notes for Magnetic Force on a Current Carrying Wire. Ampere's Force, we cover the following key points:

  • What is Ampere's Force? How it is calculated?
  • How to determine the direction of magnetic force produced when a current carrying wire is inserted inside a magnetic field?
  • How to calculate the magnetic force produced between two current carrying wires?
  • What happens when a current carrying loop is inserted inside a uniform magnetic field?
  • What is electric motor and how does it work?

Magnetic Force on a Current Carrying Wire. Ampere's Force Revision Notes

The magnetic force F produced on a conducting wire of length L when a current I flows through it, is:

F = I ∙ ( L × B )

where B is the magnetic field produced during this process.

This is a mixed product of vectors, which has the following corresponding scalar form:

F = I ∙ L ∙ B ∙ sin⁡θ

where θ is the angle between the current carrying wire and the direction of magnetic field and I, L and B are the magnitudes of the corresponding quantities regardless their direction. This force calculated either in scalar or vector form is known as the Ampere's Force.

The direction of magnetic force calculated through the formula of Ampere's Force is found by using the so-called "Fleming's Left Hand Rule". It consists of three steps:

  1. The left hand is completely open; the thumb forms an angle of 90° to the other four fingers.
  2. The four fingers show the current direction.
  3. The magnetic field lines punch the open palm.

If these three rules are applied properly, then the thumb shows the direction of magnetic force.

If we have two parallel wires of length L carrying currents I, then the magnitude field B12 produced by the first wire at the position of the second wire is

B12 = μ0 ∙ I1/2π ∙ d

and the corresponding magnetic force F12 of the first wire on the second, is

F12 = I2 ∙ B12 ∙ L2
= μ0 ∙ I1 ∙ I2/(2π ∙ d) ∙ L2

Likewise, the magnetic force F21 by which the second wire acts on the first, is

F21 = I1 ∙ B21 ∙ L1
= μ0 ∙ I1 ∙ I2/(2π ∙ d) ∙ L1

If the two wires have the same length and current, the magnitudes of the two above forces are equal. Since forces have opposite directions, the wires repel each other when parallel currents flow in them. On the other hand, when currents are antiparallel, i.e. when they have opposite directions, the two wires attract each other based on the direction of magnetic forces produced.

A current-carrying loop placed inside the magnetic field produced by two magnets with opposite poles facing each other, produces a torque when inserted properly. This is because the current flows in opposite directions in the two lateral sides of the loop. Therefore, the magnetic forces F1 and F2 are equal in magnitude and opposite in direction. If we denote by x/2 the distance from the lateral sides ab and bc to the rotating axis passing through the centre of loop, we obtain for the maximum torque τ produced:

τmax = I ∙ B ∙ L ∙ x = I ∙ B ∙ A

where A = L ∙ x is the area of loop.

Electric motor uses the interaction between electric current and magnetic field to produce motion. Basically, an electric circuit supplies the coil with electricity, while the magnetic field is provided by the two magnets between which the coil is placed. As a result, a movement in the form of torque is produced.

The output of electric motor is mechanical energy. Thus, we can say: "an electric motor is a device that converts electricity into mechanical energy."

Many electric appliances such as washing machines, vacuum cleaners, fans, air conditioners, refrigerators, etc., make use of electric motors to operate. In addition, there exist many other industrial appliances which use electric motors among which there are pumps, compressors, crushers, HVAC systems, etc.

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