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EMF Induced in a Moving Conductor

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This figure shows another way the magnetic flux can change.

It can change if aconducting loop is moved in a static magnetic field.

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.

The induced emfhas magnitude

This equation holds only if B, l, & v are mutually perpendicular. If they are not, then it is true for their perpendicular components.

Example

Does a moving plane develop a large emf?

An airplane travels at speed

v = 1000 km/h in a region where the Earth’s magnetic field is about

B = 5 10-5 T& is nearly vertical. Calculate the potential difference induced between the wing tips that are l = 70 m apart.

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.

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.

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.

If the loop is rotating with constant angular velocity ω, the induced emf is sinusoidal:

For a coil ofN loops,

Example: AC generator.

The armature of a 60-Hz ac generator rotates in a 0.15 T magnetic field. The area of the coil 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

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