Last time: how charged particles move in a magnetic field.

Consider a uniform magnetic field into the board, with conducting rod moving through it:

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+ side

- side

Charges will move

If part of a circuit, can generate a current!

Which direction is the current through the resistor?

1) Up

2) Down

Note: as rod moves, there is an increasing magnetic flux through the loop.

Magnetic Flux

Just like for electric fields, can define magnetic flux through surface:

For uniform and a flat surface :

Faraday’s LawChanging magnetic field can induce a and

where is the magnetic flux.

- Solenoid with alternating / direct current.

- Vary number of windings.

What are ways that we can increase the amount of current through the loop?

More windings?

Angle of loop relative to solenoid?

Shape of loop?

B B

Top View

Wire Loops

Solenoids

Magnetic field ~inside of solenoid only area is the same for both flux is the same for both.

In figure (a), a solenoid produces a magnetic field whose strength increases into the plane of the page. An induced emf is established in a conducting loop surrounding the solenoid, and this emf lights bulbs A and B. In figure (b), points P and Q are shorted. After the short is inserted,

1. bulb A goes out; bulb B gets brighter.2. bulb B goes out; bulb A gets brighter.3. bulb A goes out; bulb B gets dimmer.4. bulb B goes out; bulb A gets dimmer.5. both bulbs go out.6. none of the above

Lenz’s Law

The induced current creates a magnetic field that opposes the change in magnetic flux through the area enclosed by the loop.

Way to interpret the minus sign in Faraday’s Law

The current through the wire is decreasing and the loop is fixed relative to the wire. In which direction is the induced current in the loop?

1. Clockwise2. Counter-clockwise3. No current is induced

The loop shown below is traveling towards the wire with the velocity shown. The current, , is constant. In which direction is the induced current in the loop?

1. Clockwise2. Counter-clockwise3. No current is induced

The loop shown below is traveling towards the right at a constant distance from the bottom wire. The current, , is constant. In which direction is the induced current in the loop?

1. Clockwise2. Counter-clockwise3. No current is induced

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Cool Application: Generators and Motors

A uniform magnetic field can produce an EMF in a conducting loop if:1) The field changes in magnitude.2) The loop changes position within the field.3) The loop rotates within the field.4) The loop is removed from the field.5) The loop changes size.6) All of the above7) All except 2)8) All except 3)9) All except 4)

Relation to Electric Fields

Electric fields cause charges to move induced EMF can be related to :

where integral is a closed path.

Note: Not necessary for a loop to be there (i.e., test charges) for an field to be created.

Eddy Currents

Plate moving between poles of magnet:

Force tends to damp motion of the plate.

N

S

F

S

NF

Adding slots fewer paths for current higher resistance less force.

Question:

Let's say you take an ordinary wire coathanger and straighten out the hook shaped part that normally hangs over the coat rack. Now, you can spin the (roughly) triangular part around by twisting the straightened part between your fingers. Estimate the EMF that you can generate by spinning the hanger in the Earth's magnetic field (about 5.3 x 10⁻⁵ T).

Lab:

Magnetic Field of a Slinky:- Magnetic field sensor w/ LoggerPro- Do theoretical predictions about

magnetic field hold?

In terfaceV mV

Pow er supply

Sw itch

Am m eter

Quantitative Question (31.12):

A coil of 15 turns and radius 10.0 cm surrounds a long solenoid of radius 2.00 cm and 1000 turns/meter. The current in the solenoid changes as, where is in amperes and t is in seconds. Find the induced emf in the 15-turn coil as a function of time.