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23.1 Induced emf and magnetic flux  (Page 2/4)

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The figure shows a schematic diagram of an electric generator. It consists of a rotating rectangular coil placed between the two poles of a permanent magnet shown as two rectangular blocks curved on side facing the coil. The magnetic field B is shown pointing from the North to the South Pole. The two ends of this coil are connected to the two small rings. The two conducting carbon brushes are kept pressed separately on both the rings. The coil is attached to an axle with a handle at the other end. The axle may be mechanically rotated from outside to rotate the coil inside the magnetic field. Outer ends of the two brushes are connected to the galvanometer. A current is shown to flow in the coil in anti clockwise direction and the galvanometer shows a deflection.
Rotation of a coil in a magnetic field produces an emf. This is the basic construction of a generator, where work done to turn the coil is converted to electric energy. Note the generator is very similar in construction to a motor.

So we see that changing the magnitude or direction of a magnetic field produces an emf. Experiments revealed that there is a crucial quantity called the magnetic flux    , Φ size 12{Φ} {} , given by

Φ = BA cos θ , size 12{Φ= ital "BA""cos"θ} {}

where B size 12{B} {} is the magnetic field strength over an area A size 12{A} {} , at an angle θ with the perpendicular to the area as shown in [link] . Any change in magnetic flux Φ size 12{Φ} {} induces an emf. This process is defined to be electromagnetic induction    . Units of magnetic flux Φ size 12{Φ} {} are T ⋅ m 2 size 12{T cdot m rSup { size 8{2} } } {} . As seen in [link] , B cos θ = B size 12{B"cos"θ=B rSub { size 8{ ortho } } } {} ⊥ , which is the component of B size 12{B} {} perpendicular to the area A size 12{A} {} . Thus magnetic flux is Φ = B ⊥ A size 12{Φ=B rSub { size 8{ ortho } } A} {} , the product of the area and the component of the magnetic field perpendicular to it.

Figure shows a flat square shaped surface A. The magnetic field B is shown to act on the surface at an angle theta with the normal to the surface A. The cosine component of magnetic field B cos theta is shown to act parallel to the normal to the surface.
Magnetic flux Φ size 12{Φ} {} is related to the magnetic field and the area over which it exists. The flux Φ = BA cos θ size 12{Φ= ital "BA""cos"θ} {} is related to induction; any change in Φ size 12{Φ} {} induces an emf.

All induction, including the examples given so far, arises from some change in magnetic flux Φ size 12{Φ} {} . For example, Faraday changed B size 12{B} {} and hence Φ size 12{Φ} {} when opening and closing the switch in his apparatus (shown in [link] ). This is also true for the bar magnet and coil shown in [link] . When rotating the coil of a generator, the angle θ size 12{θ} {} and, hence, Φ size 12{Φ} {} is changed. Just how great an emf and what direction it takes depend on the change in Φ size 12{Φ} {} and how rapidly the change is made, as examined in the next section.

Test prep for ap courses

To produce current with a coil and bar magnet you can:

  1. move the coil but not the magnet.
  2. move the magnet but not the coil.
  3. move either the coil or the magnet.
  4. It is not possible to produce current.

(c)

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Calculate the magnetic flux for a coil of area 0.2 m 2 placed at an angle of θ =60º (as shown in the figure above) to a magnetic field of strength 1.5×10 -3 T. At what angle will the flux be at its maximum?

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Section summary

  • The crucial quantity in induction is magnetic flux Φ size 12{Φ} {} , defined to be Φ = BA cos θ size 12{Φ= ital "BA""cos"θ} {} , where B size 12{B} {} is the magnetic field strength over an area A size 12{A} {} at an angle θ size 12{θ} {} with the perpendicular to the area.
  • Units of magnetic flux Φ size 12{Φ} {} are T ⋅ m 2 size 12{T cdot m rSup { size 8{2} } } {} .
  • Any change in magnetic flux Φ size 12{Φ} {} induces an emf—the process is defined to be electromagnetic induction.

Conceptual questions

How do the multiple-loop coils and iron ring in the version of Faraday’s apparatus shown in [link] enhance the observation of induced emf?

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When a magnet is thrust into a coil as in [link] (a), what is the direction of the force exerted by the coil on the magnet? Draw a diagram showing the direction of the current induced in the coil and the magnetic field it produces, to justify your response. How does the magnitude of the force depend on the resistance of the galvanometer?

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Explain how magnetic flux can be zero when the magnetic field is not zero.

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Is an emf induced in the coil in [link] when it is stretched? If so, state why and give the direction of the induced current.

The first part of the figure shows a circular coil of wire held in a magnetic field. The magnetic field points into the paper. The coil is held using both the hands to stretch it. The second part of the figure shows the same circular coil of wire stretched in the magnetic field.
A circular coil of wire is stretched in a magnetic field.
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Problems&Exercises

What is the value of the magnetic flux at coil 2 in [link] due to coil 1?

The first part of the figure shows two single loop coils. The coil one is held vertical with a current shown to flow in anti clockwise direction. The second coil, coil two is held horizontal. The two coils are shown to be held perpendicular to each other. The second image shows a wire held vertical carrying a current in upward direction. There is a single loop coil next to the wire held horizontal.
(a) The planes of the two coils are perpendicular. (b) The wire is perpendicular to the plane of the coil.

Zero

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What is the value of the magnetic flux through the coil in [link] (b) due to the wire?

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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