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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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Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
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how many start and codon
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what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
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Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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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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