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F E = -eE. E. -. v. F B = -evB. Motional EMF. B. -. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x. -. -. -. -. -. -. eE = evB E = vB V ind = LE = LvB. v. V d t. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x. L. d.

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FE = -eE




FB = -evB

Motional EMF



x x x x x x

x x x x x x

x x x x x x

x x x x x x

x x x x x x







eE = evB

E = vB

Vind = LE = LvB


V dt

x x x x x x

x x x x x x

x x x x x x

x x x x x x

x x x x x x



Fi = LdB Ff = L(d+vdt)B

|Vind |= dF/dt

= LvdtB/dt

= LvB

motional emf
Motional emf
  • As the negative charges accumulate at the base, a net positive charge exists at the upper end of the conductor
  • As a result of this charge separation, an electric field is produced in the conductor
  • Charges build up at the ends of the conductor until the downward magnetic force is balanced by the upward electric force
  • There is a potential difference between the upper and lower ends of the conductor
motional emf cont
Motional emf, cont
  • The potential difference between the ends of the conductor can be found by
    • V = B v L
    • The upper end is at a higher potential than the lower end
  • A potential difference is maintained across the conductor as long as there is motion through the field
    • If the motion is reversed, the polarity of the potential difference is also reversed
motional emf in a circuit
Motional emf in a Circuit
  • Assume the moving bar has zero resistance
  • As the bar is pulled to the right with velocity v under the influence of an applied force, F, the free charges experience a magnetic force along the length of the bar
  • This force sets up an induced current because the charges are free to move in the closed path
motional emf in a circuit cont
Motional emf in a Circuit, cont
  • The changing magnetic flux through the loop and the corresponding induced emf in the bar result from the change in area of the loop
  • The induced, motional emf, acts like a battery in the circuit
lenz law revisited moving bar example
Lenz’ Law Revisited – Moving Bar Example
  • As the bar moves to the right, the magnetic flux through the circuit increases with time because the area of the loop increases
  • The induced current must in a direction such that it opposes the change in the external magnetic flux
lenz law bar example cont
Lenz’ Law, Bar Example, cont
  • The flux due to the external field in increasing into the page
  • The flux due to the induced current must be out of the page
  • Therefore the current must be counterclockwise when the bar moves to the right
lenz law bar example final
Lenz’ Law, Bar Example, final
  • The bar is moving toward the left
  • The magnetic flux through the loop is decreasing with time
  • The induced current must be clockwise to to produce its own flux into the page
lenz law moving magnet example
Lenz’ Law, Moving Magnet Example
  • A bar magnet is moved to the right toward a stationary loop of wire (a)
    • As the magnet moves, the magnetic flux increases with time
  • The induced current produces a flux to the left, so the current is in the direction shown (b)
lenz law final note
Lenz’ Law, Final Note
  • When applying Lenz’ Law, there are two magnetic fields to consider
    • The external changing magnetic field that induces the current in the loop
    • The magnetic field produced by the current in the loop
  • Alternating Current (AC) generator
    • Converts mechanical energy to electrical energy
    • Consists of a wire loop rotated by some external means
    • There are a variety of sources that can supply the energy to rotate the loop
      • These may include falling water, heat by burning coal to produce steam
ac generators cont
AC Generators, cont
  • Basic operation of the generator
    • As the loop rotates, the magnetic flux through it changes with time
    • This induces an emf and a current in the external circuit
    • The ends of the loop are connected to slip rings that rotate with the loop
    • Connections to the external circuit are made by stationary brushed in contact with the slip rings
ac generators final
AC Generators, final
  • The emf generated by the rotating loop can be found by

V =2 B ℓ v=2 Bℓ v sin θ

  • If the loop rotates with a constant angular speed, ω, and N turns

V = N B A ω cos ω t

  • V = Vmax when loop is parallel to the field
  • V = 0 when when the loop is perpendicular to the field
AC Generator

Angular velocity, w:

Amount of angle (radian) turned in a second

wt = total angle of turn during time t

2pf = w period T = 1/f = 2p/w

t = 0:  = 0

t = t1:  = A B sin(wt1)


Vind = - d/dt

= - ABsin(wt1)/t1

Vind = - /t

= - ABwcos(wt)

AC generation




170 V

-170 V

When we say 120 V, it means rms value!!

P  v2 or i2

vrms = 0.707va

Power Transmission

City of Gainesville has 120,000 population. On average

approximately 200 W/person of electric power is required.

Let’s assume that GRU transmit power with 120 V. How much

current Should be carried in power line?

Pt = 120,000 x 200 W = 24,000,000 W = 24 MW

P = IV, I = P/V = 24,000,000/120 = 200,000 A

However, if we deliver power with 500,000 V,

I = 24,000,000/500,000 = 48 A

Now Joule heating due to wire resistance (R) is reduced

By (48/200,000)2 = 5.8 x 10-8


Iron Core




Vp = -NpdF/dt

Vs = -NsdF/dt



Vp/Vs = Np/Ns