Chapter 22 - Electromagnetic Induction Flashcards
97Suppose the rod is moving with a speed of
5.0 m/s perpendicular to a 0.80 T magnetic
field. The rod has a length of 1.6 m and a
negligible electrical resistance. The rails
also have a negligible electrical resistance.
The light bulb has a resistance of 96 ohms.
Find:
(a) the emf produced by the rod and
(b) the current induced in the circuit
a) E = VbL
= 6.4 V
b) I = E/R
= 0.067A
In one form of Tesla coil, shown in
Figure, a long solenoid with length ℓ = 50
cm and cross sectional area A = 10 cm2
is closely wound with turns N1 =1000
of wire. A coil with turns N2 =10
surrounds it at its center
Using
B1 = u0ni
Flux is equal in both
M = Nsfs/ip
M= N2f2/i1
= N2(B1A)/i1
= N2(u0N1i1A/i1l)
= u0AN1N2/l
Plug in all the values
A = 1
N1 = 1000
N2 = 10
l = 0.50
= 25x10^-6 H
When a thin 12.0 cm iron rod moves with a constant velocity of 4.50 m/s
perpendicular to the rod in the direction shown in the following figure, the
induced emf across its ends is measured to be 0.450 V.
(b) Which point is at a higher potential, a or b?
(c) If the bar is rotated clockwise by 90° in the plane of the paper, but keeps
the same velocity, what is the potential difference induced across its
ends?
b) Force is directed towards higher potential (positive charges). Hence it points upwards, which means this end (b) has the higher potential
c) In order for there to be separation of charges, the force has to point along the length of the rod (be parallel) to induce an emf. Because force is perpendicular, no charge accumulation and hence no induced emf
A copper rod is sliding on two conducting rails that make an angle of 19° with
respect to each other, as in the drawing. The rod is moving to the right with a constant
speed of 0.60 m/s. A 0.38-T uniform magnetic field is perpendicular to the plane of the
paper. Determine the magnitude of the average emf induced in the triangle ABC during
the 6.0 s period after the rod has passed point A.
Find the base of the triangle
base = vt
= 0.60 x 6 = 3.6m
Height of triangle is base x tanx
= 1.238
Area of triangle is 1/2bh
2.23
Flux is BAcosx
x is 0 because the normal the surface and field are parallel to each other.
So BA = 0.8474 wb
Average emf = Nf/t
N = 1, use calculated flux and t = 6s
Final answer is 0.141V
A magnetic field is perpendicular to the plane of a singleturn circular coil. The magnitude of the field is changing, so
that an emf of 0.80 V and a current of 3.2 A are induced in the
coil. The wire is then re-formed into a single-turn square coil,
which is used in the same magnetic field (again perpendicular
to the plane of the coil and with a magnitude changing at the
same rate). What emf and current are induced in the square
coil?
The only thing that is changing between the two is the area
Calculate L
for circle: L = 2πr
r = L/2π
Area = L^2/rpi
for square: L = 4s
s = L/4
Area = L^2/16
Find the ratio of the areas
new emf = old emf x (new area/old area)
Area of square/area of circle
= pi/4 = 0.785
new emf = 0.8 x 0.785
Resistance is the same so
R = 0.80/3.2 A
isquare = 0.628V/0.25 = 2.51
What is the equation for energy dissipation?
Energy dissipated = power dissipated x time
A 30.0 cm x 60.0 cm rectangular circuit containing a 15 Ω resistor is perpendicular to a uniform magnetic
field that starts out at 2.65 T and steadily decreases at 0.25 T/s (See Figure). While this field is changing,
what does the ammeter read?
x = 0 degrees so cosx = 1
V = ∆Φ/∆t
A is constant and B is changing so
V = A(∆B/∆t) and this rate of change is 0.25T as outlined in teh question
V = (0.3)(0.6)(0.25) = 0.045V
I = V/R
Define electromagnetic induction
Changing magnetic flux or changing area/location of coil in constant magnetic filed induces emf
Outline Lenz’s law
- Change in magnetic flux induces current (determined by RHR#2), this induced current induces its own magnetic field which opposes in direction the change in original magnetic flux
If flux increases, induced magnetic field points in opposite direction to oppose increase
If flux decreases, induced field points in same direction as flux to try to restore it
How do you determine polairity?
1) Determine whether flux is increasing/decreasing to determine direction of induced magnetic field
2) Use RHR#2 to determine direction of induced current
3) Polarity (pos/neg terminal) can be assigned because conventional current from pos to neg
As shown in the figure below, a conductor bar starts from rest and slides vertically down along a
conductor track while maintaining good contact. The uniform magnetic field is 0.20𝑇 in the
whole space. The width of the track is 0.50𝑚. The mass of the bar is 0.10𝑘𝑔. The resistance of
the track is negligible, but the resistance of the bar is 3.0𝛺. For all calculations below, ignore air
resistance and friction.
[ /2] 3. a) Calculate the induced current in the bar when the bar reaches a constant falling speed under the
combined influence of its gravity and the magnetic force.
[ /2] 3. b) Calculate the constant speed at which the bar can fall under the combined influence of its gravity
and the magnetic force
a) At constant speed, magnetic force balances gravity
Fb = Fg
mg = ILB
Angle between current and magnetic field is 90 so sin90 is 1
I = mg/lb
= 9.8A
b)
Induced emf: E = Blv
Om’s Law: I = E/R
v = IR/bl
294m/s
