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Physics Lesson 16.5.4 - Work Done on a Magnetic Dipole

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Welcome to our Physics lesson on Work Done on a Magnetic Dipole, this is the fourth lesson of our suite of physics lessons covering the topic of Magnetic Dipole Moment, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Work Done on a Magnetic Dipole

If an external force rotates the coil (magnetic dipole) from an angle θ1 to another angle θ2, a resulting torque is produced. This action results in a work W done on the dipole by the applied torque. If the dipole is stationary before and after the change in the angle mentioned above, then the work done on the magnetic dipole is

W = Ufinal - Uinitial

There are many more examples of magnetic dipoles besides the circular or rectangular current carrying loops discussed so far. For example, a charged rotating sphere can be a magnetic dipole, subatomic particles such as protons and electrons can be considered as magnetic dipoles as well because they have magnetic dipole moments and so on. All these quantities can be viewed as tiny current carrying loops.

Example 4

The figure below shows a lateral view of a circular coil containing 100 turns. The coil's diameter is 4 cm and a 200mA current is flowing through it. The coil is initially at rest inside a 0.500 T magnetic field at the position 1 shown in the figure. Then it rotates by means of an external force at the position 2.

Physics Tutorials: This image provides visual information for the physics tutorial Magnetic Dipole Moment

Calculate:

  1. The direction of electric current flowing through the coil
  2. The work done by the external force to move the coil from position 1 to position 2

Solution 4

  1. Applying the right hand rule where the thumb is in the direction of magnetic dipole moment μ and the four fingers show the direction of current, it is obvious that the current in = Physics Tutorials: This image provides visual information for the physics tutorial Magnetic Dipole Moment
  2. We have the following clues:

    θ1 = 0°
    θ2 = 90°
    d = 4 cm = 0.04 m
    I = 200 mA = 0.200 A
    B = 0.500 T
    N = 100
    W = ?

    From the equation
    W = ∆U = Uf - Ui
    = U(θ2 ) - U(θ1 )
    = [-μ ∙ B ∙ cos⁡θ2 ] - [-μ ∙ B ∙ cos⁡θ1 ]
    = [-N ∙ I ∙ A ∙ B ∙ cos⁡θ2 ] - [-N ∙ I ∙ A ∙ B ∙ cos⁡θ1 ]
    = [-N ∙ I ∙ A ∙ B ∙ cos⁡900 ] - [-N ∙ I ∙ A ∙ B ∙ cos⁡00 ]
    = [-N ∙ I ∙ A ∙ B ∙ 0] - [-N ∙ I ∙ A ∙ B ∙ 1]
    = N ∙ I ∙ A ∙ B
    = N ∙ I ∙ π ∙ (d/2)2 ∙ B
    = 100 ∙ (0.200A) ∙ 3.14 ∙ (0.04m/2)2 ∙ (0.500T)
    = 0.01256 J
    = 12,56 mJ

You have reached the end of Physics lesson 16.5.4 Work Done on a Magnetic Dipole. There are 4 lessons in this physics tutorial covering Magnetic Dipole Moment, you can access all the lessons from this tutorial below.

More Magnetic Dipole Moment Lessons and Learning Resources

Magnetism Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial		Revision
Notes		Revision
Questions
16.5Magnetic Dipole Moment
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
16.5.1What is Magnetic Moment? Magnetic Dipole Moment
16.5.2Torque in Terms of Magnetic Dipole Moment
16.5.3Energy of a Magnetic Dipole
16.5.4Work Done on a Magnetic Dipole

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