Do now: V = BvL

a) Calculate the induced voltage across the rollerV = BvL = 0.46 x 0.25 x 0.24 = 0.0276 = 28mV (2 s.f.)

b) Calculate the size and direction of the induced currentV = IR I = V/R = 0.0276 / 12 = 2.3mA (out of page)

c) When the current is induced in the roller, the roller slows down. Explain why.A current carrying wire in a magnetic field experiences a force (F = BIL) which opposes the motion causing it. This is Lenz’s Law, and is required by conservation of energy: mechanical energy has been transformed into electrical energy, so therefore the mechanical energy must drop.

A roller is moved at 0.25ms-1 along metal rails through a 0.46T magnetic field. The rails are 24cm apart and a 12Ω resistor connects cross them to complete the circuit.

Lenz’s Law

“The coil tries to oppose the force of the magnet”

The coil does not have the opposite pole to the magnet!

Lenz’s LawLenz’s LawThe direction of the induced current is The direction of the induced current is such that it creates an opposing force on such that it creates an opposing force on the motion that is causing it.the motion that is causing it.

Opposing Force F=BIL

Direction of movement

Induced current I

Try Activity 15A - just Question 1!

Then go back, read and take note on pages 249 – 255 (especially “flux” and then try the rest of Activity 15A)

Which will generate a larger Which will generate a larger induced voltage? induced voltage?

Magnetic flux Magnetic flux Φ Φ is the is the magnetic field strength magnetic field strength B B passing through an area A passing through an area A (perpendicular to the field) (perpendicular to the field)

ΦΦ = B x A or B = = B x A or B = ΦΦ / A / A

The unit for magnetic flux is The unit for magnetic flux is the the Weber WbWeber Wb

A change in flux creates A change in flux creates an induced voltage an induced voltage

Magnetic FluxMagnetic Flux

A useful analogy is using A useful analogy is using a net to catch whitebait a net to catch whitebait in a stream….in a stream….

If you don’t hold the net If you don’t hold the net straight up and down, straight up and down, you don’t catch many you don’t catch many whitebait!!whitebait!!

A change in flux creates A change in flux creates an induced voltagean induced voltage

(the whitebaiter reacts!)(the whitebaiter reacts!)

We know that the induced voltage is V=BvLWe know that the induced voltage is V=BvL

How is this related to the change in flux How is this related to the change in flux ΦΦ ? ?

Initially, Initially, ΦΦ = 0 through the loop because the area of the loop in the field is zero….. = 0 through the loop because the area of the loop in the field is zero…..

LSpeed v

So:So:

ΔΦΔΦ = B x = B x ΔΔAA

ΔΦΔΦ = B x (vt x L) = B x (vt x L)

= (BvL) x t= (BvL) x t

But V = BvLBut V = BvL

So So ΔΦΔΦ = V x t = V x t

Or V = Or V = ΔΦΔΦ / t / t

L A v

Some time t later, A has changed by Some time t later, A has changed by

ΔΔA = A = (vt x L)(vt x L)

Faraday’s LawFaraday’s LawThe induced voltage in a conductor is determined The induced voltage in a conductor is determined by the by the rate of change of fluxrate of change of flux

tV

The negative sign is a

reminder of Lenz’s Law

If flux doesn’t change, then there is no induced V

How can the flux change?How can the flux change?

Φ = B x A

By changing the area of the loop By changing the area of the loop

in B, or by changing B itselfin B, or by changing B itself

Yesterday we used V = BvL to calculate the size of V and the direction of the induced current as the loop:

• enters the magnetic field

• is completely in the field

• leaves the field

V = 0.80 x 0.10 x 0.50 = 0.040V, anticlockwise

V = 0 (AB cancels BC)

V = 0.040V, clockwise

flux increases, as loop enters B

no change in flux, when loop fully inside B

flux decreases, as loop leaves B

Activity 15A Let’s destroy some more

watermelons!