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EMF Induced in a Moving Conductor (“ Motional EMF ”)

EMF Induced in a Moving Conductor (“ Motional EMF ”). This figure shows another way the magnetic flux can change. It can change if a conducting loop is moved in a static magnetic field.

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EMF Induced in a Moving Conductor (“ Motional EMF ”)

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  1. EMF Induced in a MovingConductor (“Motional EMF”)

  2. This figure shows another way the magnetic flux can change. It can change if aconducting loop is movedin a static magnetic field.

  3. The induced current in the figure is in a direction that tends to slow the moving bar. That is, It takes an external force to keep it moving.

  4. The induced emfhas magnitude • This • holds ONLY if B, l, & v are mutually perpendicular. • If they are not, then it is true for • their perpendicular components.

  5. Induced emfmagnitude: Example: Does a moving plane develop a largeemf? • A plane travels at speed v = 1000 km/h • in a region where Earth’s magnetic • field B = 5  10-5 T& is nearly vertical. • Calculatethe potential difference • induced between the wing tips that • are l = 70 m apart. Solution:  = B l v  1 V

  6. Example • Electromagnetic Blood-flow measurement • The rate of blood flow in our body’s vessels can be • measured using the apparatus shown, since blood • contains charged ions. Suppose that the blood vessel is • 2.0 mm in diameter, the magnetic field is 0.080 T, & the • measured emf is 0.10 mV. • Calculate the flow • velocity v of the blood.

  7. Example: Force on a rod. • To make the rod move to the right at speed v, you • need to apply an external force on the rod to the right. • Calculate • (a) The magnitude of the required force. • (b) The external power needed to move the rod.

  8. Motional emf Motional emf is the emf induced in a conductor moving through a constant magnetic field. • Electrons in the conductor experience a • force that is directed along ℓ:.

  9. Under this force, electrons move to the lower end of the conductor & accumulate there. As a result of this charge separation, an electric field is produced inside the conductor. The charges accumulate at both ends of the conductor until they are in equilibrium with regard to the electric and magnetic forces. At equilibrium, qE = qvB or E = vB.

  10. As a result of this charge separation, an electric field is produced inside the conductor. qE = qvB or E = vB. This electric field is related to the potential difference across the ends of the conductor: V = E ℓ =B ℓ v. This potential difference is maintained between the ends of the conductor as long as it continues to move through the uniform magnetic field. If the direction of the motion is reversed, the polarity of the potential difference is also reversed.

  11. Sliding Conducting Bar A conducting bar moving through a uniform field and the equivalent circuit diagram. Assume the bar has zero resistance. The stationary part of the circuit has a resistance R.

  12. Sliding Conducting Bar • The induced emf is • Since the resistance in the circuit is R, the current is

  13. Sliding Conducting Bar • The applied force does work • on the bar. It moves the • charges through a magnetic • field & establishes a current. • The change in energy of the system during some time interval • must be equal to the transfer of energy into the system by work. • The power input is equal to the rate at which energy is • delivered to the resistor.

  14. More on Lenz’s Law • Faraday’s Lawsays that the induced emf & the change in magnetic flux have opposite algebraic signs. This has a physical interpretation known as Lenz’s Law. Lenz’s Law: The induced current in a loop is in the direction that creates a magnetic field that opposes the change in magnetic flux through the area enclosed by the loop. • The induced current tends to keep the original magnetic flux through the circuit from changing.

  15. Lenz’ Law, Example • The conducting bar slides on the two fixed conducting rails. • The magnetic flux due to the external magnetic field through the enclosed area increases with time. • The induced current must produce a magnetic field out of the page. So, the induced current must be counterclockwise. • If the bar moves in the opposite direction, the direction of the induced current will also be reversed.

  16. Electric Generators A generatoris the opposite of a motor. It transforms mechanical energy into electrical energy. The figure shows an ac generator: The axle is rotated by an external force such as falling water or steam. The brushes are in constant electrical contact with the slip rings.

  17. If the loop is rotating with constant angular velocity ω, the induced emf is sinusoidal: For a coil ofN Loops:

  18. Example: AC generator. The armature of a 60-Hz ac generator rotates in a 0.15 T magnetic field. The coli area is 2.0  10-2 m2, Calculate the number of loops needed for the peak output to be E = 170 V. A dc generator is similar to an ac generator, except that it has a split-ring commutator instead of slip rings. AC DC

  19. Automobiles now use alternators rather than dc generators, to reduce wear.

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