Physics 2

1
Physics 2

• Chapter 20
• Section 1

2
Demonstration Notes

• As magnet approaches the coil the B field in the
  coil increases and a I is produced
• As magnet leaves the coil the B field in the coil
  decreases and a I is produced in the opposite
  direction
• Similar results are achieved when the coil moves
  instead

3
Induction

• Induced current - current brought about by a
  changing magnetic field
• To get a current you need an emf
• Induced emf emf brought about by a changing
  magnetic field

4
Ways to Induce an emf and a Current

• Change the strength of the magnetic field through
  the coil
• - as magnet moves closer the B field
  increases
• - as magnet moves away the B field decreases

5
Ways to Induce an emf and a Current

• Change the area of the coil in a uniform B field
• - decreasing area decreases B field passing
  through
• - increasing area increases B field passing
  through

6
Ways to Induce an emf and a Current

• Rotate the coil in a uniform B field
• - as the coil rotates the amount of B field
  perpendicular to the coils area changes
• Remember even if your coil is not part of a
  complete circuit, an emf will still be induced
• to have a current the coil has to be part of
  a complete circuit

7
Motional emf

• X X X X X
• X X X X X
• v
• X X X X X
• X X X X X

• Every q in rod as v to the right so feels F up
  the rod
• q collects at the top and forms an emf (or
  potential difference)
• q will stop moving when F between and charges
  balances F due to B field

8
Motional emf

• emf in rod brought about due to motion of charges
  in a B field
• - exists as long as rod moves

• X X X X X
• X X X X X
• v
• X X X X X
• X X X X X

9
Motional emf

• X X X X X
• X X X X X
• X X X X v X
• X X X X X

• Consider a rod sliding on conducting rails
• q moves counter-clockwise around loop as long as
  rod moves
• ? vBl
• where v speed
• B mag field
• l length of rod

A
V
10
Electromagnetic Induction

• Producing an induced emf with the aid of a
  magnetic field
• 1 problem with our arrangement!
• I in rod is perpendicular to B field so
  experiences a force opposing the rods velocity
• To keep rod moving an external force will need to
  be applied

• 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 X X X X X
• X X X X X X X

11
Sample Problem

• Suppose a rod is moving at a speed of 5 m/s in a
  direction perpendicular to a 0.8 T B field. The
  rod has a length of 1.6 m and has negligible
  electrical resistance. What is the emf of the
  rod? Assuming a light bulb having a resistance
  of 96 ohms is connected, find the induced current
  in the circuit. What force opposes the motion of
  the rod?

12
Magnetic Flux

• ? BA cosT ? Tm2 Weber, Wb
• Where ? magnetic flux
• B magnitude of magnetic field at
• surface
• A area of the surface
• T angle between B and the normal
• to the surface

13
Sample Problem

• A rectangular coil of wire is situated in a
  constant B field whose magnitude is 0.5 T. The
  coil has an area of 2 m2. Determine the magnetic
  flux for the orientations of 0, 60, and 90
  degrees.

14
Magnetic Flux

• Magnetic flux is proportional to the number of B
  field lines that pass through a surface
• In part c of our example no lines passes through
  the loop so there was no flux

15
Review

• Electromagnetic induction an emf is brought
  about by the use of a B field
• Induced emf voltage brought about by changes in
  a B field
• Motional emf voltage brought about by motion
  through a B field
• An induced or motional emf can produce an induced
  current if connected to a closed pathway.

16
Sample Problem

• Assume that R 6 ohms, l 1.2 m, and that a
  uniform 2.5 T magnetic field is directed into the
  page. At what speed should the bar be moved to
  produce a current of 0.5 A in the resistor?

• F

17
Sample Problem

• Assume the resistor has a value of 6 ohms. A 2.5
  T magnetic field is directed into the paper. Let
  l 1.2 m and neglect the mass of the bar.
  Calculate the force required to move the bar to
  the right at a constant speed of 2 m/s.

• F

18
Sample Problem

• A 5 sided object whose width is 0.4 m, length is
  1.2 m, height is 0.3 m, and slanted face is 0.5
  m, is placed in a uniform B field. The B field
  has a magnitude of 0.25 T and points along the y
  direction. Determine the magnetic flux for each
  of the 5 sides.

• y
• B
• x

19
Faradays Law of Electromagnetic Induction

• The avg emf induced in a coil of N loops during a
  time ?t is N times the ?f through each loop
  divided by the time
• ? -N (?f / ?t)
• Since f BAcosT we get E if B, A or T
• change in any way

20
Sample Problem

• A coil of wire consists of 20 turns, each of
  which has an area of 0.015 m2. A constant B
  field is perpendicular to each loop. At time t
  0, the magnitude of the B field at the location
  of the coil is 0.05 T. At a time of t 0.1 s,
  the B field at the coil is now 0.06 T. Find the
  average emf induced in the coil during this time.
  What would be the value of the induced emf if
  the magnitude of the B field decreased from 0.06
  T to 0.05 T in 0.1 s?

21
Sample Problem

• A flat coil of wire has an area of 0.02 m2 and
  consists of 50 turns. At t 0 the coil is
  oriented so its surface is perpendicular to a
  constant B field of magnitude 0.18 T. The coil
  is then rotated through an angle of 30 degrees in
  a time of 0.1 s. Determine the average emf
  induced. What would be the induced emf if the
  coil were returned to its initial orientation in
  the same time of 0.1 s?

22
Lenzs Law

• Polarity of an induced emf is such that the emf
  would produce a current whose own B field opposes
  the change in flux that causes the induced emf
• induced B field opposes the change in flux, not
  the flux itself

23
Lenzs Law

• To use Lenzs Law
• Determine whether the flux is increasing or
  decreasing
• Find what direction of induced B will oppose the
  change in flux
• Use RHR to determine the direction of induced
  current

24
Sample Problem

• R

• The figure shows a permanent magnet approaching a
  loop of wire. The external circuit attached to
  the loop consists of the resistance R. Find the
  direction of the induced current and the polarity
  of the induced emf.

S N
25
Sample Problem

• 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

• There is a constant B field in a rectangular
  region of space. The field is directed
  perpendicular to the plane of the paper. Outside
  this region there is no B field. A copper ring
  slides through this region, from position 1 to
  position 5. For each of the 5 positions,
  determine if an induced I exists in the ring and,
  if so, the direction of the induced I.

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