Electromagnetic Induction

Question 1

Define magnetic flux φ. Give equation and SI unit

Answer 1

mag flux thru plane surface is pdt of flux density normal to surface & area of surface

mag flux thru area, φ = BA

SI Unit: weber (Wb)

*Scalar, not vector like mag flux density

Question 2

Define magnetic flux linkage, Nφ. Give equation

Answer 2

mag flux linkage thru coil of N turns is pdt of no of turns N of coil & mag flux φ linking each turn

If coil of N turns is placed in a region w uniform B field, then flux linkage thru coil Nφ

Nφ = NBA

(B is normal to surface component)

• SI unit still weber (Wb)

Question 3

What are the factors that determine magnitude of induced e.m.f.?

Answer 3

• change B field
• change orientat n of coil
• change cross-sectional area
• change no of coil

Question 4

Does induced e.m.f. always mean induced current?

Answer 4

Not necessarily
- There can be induced emf w/o current
(Like battery not in a closed circuit)
- current flows oni when coil is part of closed circuit

Question 5

Define Faraday’s Law. Give formulae

Answer 5

states that induced emf is directly proportional to rate of change of mag flux linkage

ε=- d(Nφ)/dt
where
ε is induced emf,
N is no of turns in coil
φ is mag flux thru coil

For N turns coil w mag flux φ thru coil, magnitude of induced emf is

|ε|= |N dφ/dt|

Question 6

Define Lenz’s Law

Answer 6

States direct n of induced emf is such as to cause effects to oppose change producing it

Question 7

(EMI) What is the 3 step approach for closed loop?

Answer 7

1. Direct n of flux linkage? (Thru loop)
   Change? (Increase/decrease)
   Due to? (N, B, A or θ)
2. Apply Faraday’s Law
   - mag flux linkage change
   => induces emf
3. If closed circuit, induced emf cause induced current
   - Apply Lenz’s Law to determine direct n of current
   => flows in direct n to produce effect to oppose change in mag flux linkage

Question 8

What is the formula for magnitude of induced e.m.f along straight conductor

Answer 8

where
B, l, v perpendicular to one another,
l is length of conductor
v is speed of conductor

ε | = Blv

Question 9

What is the formula for potential difference across ends of an isolated straight conductor?

Answer 9

ΔV = Blv

*on conductor

Question 10

(EMI) What is 3 step thinking strategy for isolated conductor?

Answer 10

1. What motion cause change in mag flux?
2. What is direct n of current due to motion of e- in conductor
3. Apply Fleming’s left hand rule determine direct n of force on e-

Question 11

What is formula of magnitude of induced e.m.f. across one spoke of rotating disk?

Answer 11

where
r is length of spoke (radius of disk),
f is frequency of revolut n

ε | = Bπr²f

Question 12

Explain direction of induced e.m.f. of rotating disc

Answer 12

Consider e- within one of radial sect n as disc rotate, w instant velocity tangential of e- to its motion
-By FLHR, e- experience force Fb toward rim of disc, migrate in that direct n
- if external circuit connected across center & rim, current can flow
- if no external circuit connected, e- accumulate at rim of disc, and set up e- field
- as more e- accumulate at rim, e- field bcome stronger & migrat n of e- stop when Fe=Fb. An eqm is reached
- ctr of disc thus hv net +ve charge while rim net -ve charge

NOTE: Can use Fleming’s Right Hand Rule as shortcut but NOT for expl n

Question 13

Explain formation of eddy currents

Answer 13

• When thick/broad piece conductor enter/leave B field, induced currents can b generated in separate loop within diff part of conductor
• Such induced current r called eddy currents, which dissipate energy, create B field that tend oppose change in B field

Question 14

Explain how A.C. generator works

Answer 14

• as loop rotate, mag flux through it change w time, inducing emf & current in external circuit
• ends of loop connected to slip rings that rotate w loop
• connect n to external circuit made by stationary brushes in contact w slip ring

*current reverses direct n every time plane of loop pass vertical pos n

Question 15

What is formula for maximum induced emf?

Answer 15

ε max = NBAω

where
ω is angular velocity (θ/t)

Question 16

How do induction cookers work?

Answer 16

• use eddy current
• alternating current flow thru conducting coil below cooking surface
• oscillating B field generated induces eddy currents in base of conducting cooking pan
• electrical energy dissipated due to these currents is converted into thermal energy to cook food

Question 17

How do electromagnetic brakes in cars work?

Answer 17

• a conducting braking disc is fixed to axle of wheel
• part of braking disc is placed btw pole of e-magnet
• as disc rotate, every radial segment of disc continuously cuts mag flux, cause induced eddy currents within it
• these induced currents create mag force opposing turning motion of disc & thus wheel
• extent of braking effect can be controlled by adjusting magnitude of current via brake pedal

Question 18

How do electromagnetic brakes in trains on wheels work?

Answer 18

• e-magnet hang fr train undercarriage near 1 rail. Large current is sent thru coil of e-magnet
• as current pass thru e- magnet, B field set up due to presence of current
• B field lines due to moving e-magnet cause changing mag flux linkage on diff segment on rail
• by Faraday’s Law, emf generated in rail
• By Lenz’s law, induced current in segment of rail cause resistive force act on e-magnet
  => train decelerate

Question 19

How do vending machine coin chute work?

Answer 19

• when coin enter slot, electrical resistance being checked at holder A by apply pd
• if resistance acceptable, coin continue down inlet track
• along track, 2 magnet induce eddy current in coin, slow down speed
• how much coin slows depend on metal composit n
• speed sensor check coin speed
• if acceptable speed, gate B open up, coin accepted
• else, gate C open up, coin rejected

Question 20

How do ground fault interruptors work?

Answer 20

• safety device protecting ppl against electric shock (make use of Faraday’s law)
• when fault occur, some current may flow out of device, cause return current b diff fr supply current
• diff in current btw 2 wire produce net B field
• resultant change in mag flux thru sensing coil induce emf, so induced current flow to circuit breaker
• circuit breaker break electrical connect n to prevent accident

Question 21

How do electric guitars work?

Answer 21

• pickup coil placed near vibrating guitar string, made of metal that can b magnetised
• inside pickup coil, permanent magnet magnetise portion of string nearest to pickup coil
• when guitar string struck, vibrating magnetised portion cause changing mag flux thru pickup coil
• induced emf & current in coil, which is fed to amplifier
• output of amplifier is sent to loudspeaker