EMF Induced in a Moving Conductor Motional EMF

EMF Induced in a Moving Conductor (“Motional EMF”) Copyright © 2009 Pearson Education, Inc.

This figure shows another way the magnetic flux can change. It can change if a conducting loop is moved in a static magnetic field. Copyright © 2009 Pearson Education, Inc.

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. Copyright © 2009 Pearson Education, Inc.

• The induced emf has magnitude • This holds ONLY if B, l, & v are mutually perpendicular. • If they are not, then it is true for their perpendicular components. Copyright © 2009 Pearson Education, Inc.

Induced emf magnitude: Example: Does a moving plane develop a large emf? • 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. • Calculate the potential difference induced between the wing tips that are l = 70 m apart. Solution: Copyright © 2009 Pearson Education, Inc. =Blv 1 V

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 m. V. • Calculate the flow velocity v of the blood. Copyright © 2009 Pearson Education, Inc.

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. Copyright © 2009 Pearson Education, Inc.

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: . Copyright © 2009 Pearson Education, Inc.

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, q. E = qv. B or E = v. B. Copyright © 2009 Pearson Education, Inc.

As a result of this charge separation, an electric field is produced inside the conductor. q. E = qv. B or E = v. B. 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. Copyright © 2009 Pearson Education, Inc.

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. Copyright © 2009 Pearson Education, Inc.

Sliding Conducting Bar • The induced emf is • Since the resistance in the circuit is R, the current is Copyright © 2009 Pearson Education, Inc.

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. Copyright © 2009 Pearson Education, Inc.

More on Lenz’s Law • Faraday’s Law says that the induced emf & the change in magnetic flux have opposite algebraic signs. This has a physical interpretation known as 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. Copyright © 2009 Pearson Education, Inc.

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. Copyright © 2009 Pearson Education, Inc.

Electric Generators A generator is 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. Copyright © 2009 Pearson Education, Inc.

If the loop is rotating with constant angular velocity ω, the induced emf is sinusoidal: For a coil of N Loops: Copyright © 2009 Pearson Education, Inc.

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 m 2, 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 Copyright © 2009 Pearson Education, Inc. DC

Automobiles now use alternators rather than dc generators, to reduce wear. Copyright © 2009 Pearson Education, Inc.