**Examples for induction**

Example #1

Problem:

An airplane moves such that its
velocity and wingspan are both perpendicular to a magnetic field of 1.0E-4*
T*. How fast must the plane move to generate a potential difference of
12 *V* between the wing tips?
(DATA: wingspan=36.0 *m*.)

Solution:

** V = v L B**, put in the
numbers and solve for

* v = *3.3E3

Example #2

Problem: Consider the loops shown above. A
magnetic field of 0.5 *T* is introduced into the loop over a time * t*.
If the radius of a loop is 4.0

Solution:

Use Faraday's law:

The change in the magnetic field is 0.5 *T*
and everything else is given, so solve for
**D***t*
which is the time over which the field is
introduced * t*.

* t = *0.126

Example #3

Problem: Consider the loops shown above
which are immersed in a constant magnetic field of 0.5 *T*. The radius of the loop
is 3.0 *cm*. If the loop is rotated at 60 *Hz*, how many turns are needed to
achieve an r.m.s.voltage of 110 *V*?

Solution:

The rate of change of the flux is

We want an r.m.s. voltage, which is the maximum voltage times 1/sqrt(2).

* N *=
292

Example #4

Problem: Consider the transformer shown
above. The r.m.s. voltage of the primary source is 110 *V*, and there are 100 turns
in the primary loop compared to 500 turns in the secondary loop. What is the power
consumed in the 10 W resistor?

Solution:

The voltage of the secondary source is (500/100) times
larger, * V_{s}* = 550

* P *=
30.25

Example #5

Problem:

a.) Consider a solenoid which
has zero current at * t* = 0, and is then ramped up
to 2.0 amps in 1.5

Solution:

Use
*V* = *L***D****I /****D**** t**
to find

* L*
= 0.0105

b.) What is the final energy stored in the solenoid?

Solution:

Use
** U = (1/2) L I^{2}**
to find

* U*
= .021

Example #6

Problem: Consider the two circuits, * A*
and

1.) Which circuit(s) have a current in the
instant immediately after * t* = 0 ?

2.) Which circuit(s) have a current a long
time after * t* = 0 ?

3.) Which element(s) (aside from the
battery) store energy a long time after * t* = 0 ?

* A*,

Example #7

Problem: Consider an inductor created by
coiling ** N** turns of wires around a cylinder of radius

1.) What happens to the inductance if the length is doubled?

2.) What happens to the inductance if the number of turns is doubled?

3.) What happens to the inductance if the radius is doubled?

The inductance is
(halved to 0.0125 *H*, quadrupled to 0.1 *H*, quadrupled to 0.1
*H*)

*
Examples
Induction index
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