Transcript As the source current increases with time, the magnetic flux

Slide 1
Fig 32-CO, p.1003

As the source current increases with time,
the magnetic flux through the circuit loop
due to this current also increases with
time. This increasing flux creates an
induced emf in the circuit.

The direction of the induced emf is such
that it would cause an induced current in
the loop (if a current were not already
flowing in the loop), which would
establish a magnetic field that would
oppose the change in the source magnetic
Slide 2
field.
  - d/dt
After the switch is closed, the current
produces a magnetic flux through the
area enclosed by the loop.
As the current increases toward its
equilibrium value, this magnetic flux
changes in time and induces an emf in
the loop.
Slide 3
For N turns coil
From (1)
where L is a proportionality constant—called the inductance of
the coil
Slide 4
(a) A current in the coil produces a magnetic field directed to the
left.
(b)If the current increases, the increasing magnetic flux creates an
induced emf having the polarity shown by the dashed battery.
(c) The polarity of the induced emf reverses if the current
decreases.
Slide 5
Fig 32-2, p.1005
Inductance : a self-induced emf is always proportional
to the time rate of change of the source current.
Slide 6
p.1005
Slide 7
Slide 8
Slide 9
Ex: A air core solenoid contains 500 turns with a length 40 cm and a cross
sectional area 6 cm2 Then the self-inductance is
0.471 mH
L
 oN 2 A
l
A 200 mH inductor carriers a steady current of 0.5 A . When the switch in
the circuit is opened the current is effectively zero after 10 mS. What is the
induced electromotive force emf in The inductor during this time
10 mV
Slide 10
RL circuit consists of battery are
connected to a resistor and an inductor
Suppose that the switch S is thrown
closed at t =0. The current in the circuit
begins to increase, and a back emf that
opposes the increasing current is
induced in the inductor.
The back emf is
we can apply Kirchhoff’s loop rule to this circuit,
traversing the circuit in the clockwise direction
Slide 11
dI
 L L
dt
dI
  IR  L
0
dt
by apply Kirchhoff’s loop rule to this circuit,

dI
 0
dt
If we multiply each term by I and rearrange
the expression, we have
 IR  L
This expression indicates that the rate at which energy is supplied by the
battery equals the sum of the rate at which energy is delivered to the
dI
resistor I2R, , and the rate at which energy is stored in the inductor, LI
dt
If we let U denote the energy stored in the inductor at any time, then we
can write the rate dU/dt at which energy is stored as
Slide 12
We can also determine the energy density of a magnetic field.
For simplicity, consider a solenoid whose inductance is given by
The magnetic field of a solenoid is given by Equation
Slide 13
Slide 14
Energy stored in a parallel-plate capacitor
Ch 26
For a parallel-plate capacitor, the potential difference is related to the
electric field through the relationship V = Ed.. The capacitance is given by
A
C 0
d
By substituting
1
1
A
2
U  C V  ( 0
) ( Ed ) 2
2
2
d
1
  0 ( Ad ) E 2
2
The energy per unit volume known as the energy density, is
U
UE 
 12  0E 2
Ad
The energy density in any electric field is proportional to the square of the
magnitude of the electric field at a given point
Slide 15
Ex: A long solenoid has a self inductance of 5 H . The energy stored in its
magnetic filed when it carries a current of 10 A is :
250 J
A long solenoid has a self inductance of 10  H. The energy stored in its
magnetic filed when it carriers a current of 10 A is:
500 J
Ex: If the magnetic filed is 15 mT , what is the magnetic energy density
89.57
Slide 16
The volume energy density In a space due to a magnetic filed of 0.5T equals:
100,000
The volume energy density stored in a magnetic filed B is proportional to:
Slide 17
If UE is the energy density resulted from an applied electric filed E
And UB is the energy density from an applied magnetic filed B, then the ratio
UE/UB will be
The electric energy density
Slide 18
UE
U

 12  0E 2
Ad
Slide 19
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Slide 26
B  I
B  K I
L   N
Slide 27
d
d  dI
 N
dt
dI dt
dI
N K
dt
dI
L   L
dt