(a) 
The relationship between frequency and wavelength of an electromagnetic wave is given by
where
is the speed of light
is the frequency
is the wavelength
In this problem, we are considering light with wavelength of
Substituting into the equation and re-arranging it, we can find the corresponding frequency:
(b) 
The period of a wave is equal to the reciprocal of the frequency:
And using 
as we found in the previous part, we can find the period of this wave:
Answer:
Given the area A of a flat surface and the magnetic flux through the surface 
it is possible to calculate the magnitude 
.
Explanation:
The magnetic flux gives an idea of how many magnetic field lines are passing through a surface. The SI unit of the magnetic flux is the weber (Wb), of the magnetic field B is the tesla (T) and of the area A is (
). So 1 Wb=1 T.m².
For a flat surface S of area A in a uniform magnetic field B, with 
being the angle between the vector normal to the surface S and the direction of the magnetic field B, we define the magnetic flux through the surface as:
We are told the values of and B, then we can calculate the magnitude
Answer:
a) fem = - 2.1514 10⁻⁴ V, b) I = - 64.0 10⁻³ A, c) P = 1.38 10⁻⁶ W
Explanation:
This exercise is about Faraday's law
fem = 
where the magnetic flux is
Ф = B x A
the bold are vectors
A = π r²
we assume that the angle between the magnetic field and the normal to the area is zero
fem = - B π 2r dr/dt = - 2π B r v
linear and angular velocity are related
v = w r
w = 2π f
v = 2π f r
we substitute
fem = - 2π B r (2π f r)
fem = -4π² B f r²
For the magnetic field of Jupiter we use the equatorial field B = 428 10⁻⁶T
we reduce the magnitudes to the SI system
f = 2 rev / s (2π rad / 1 rev) = 4π Hz
we calculate
fem = - 4π² 428 10⁻⁶ 4π 0.10²
fem = - 16π³ 428 10⁻⁶ 0.010
fem = - 2.1514 10⁻⁴ V
for the current let's use Ohm's law
V = I R
I = V / R
I = -2.1514 10⁻⁴ / 0.00336
I = - 64.0 10⁻³ A
Electric power is
P = V I
P = 2.1514 10⁻⁴ 64.0 10⁻³
P = 1.38 10⁻⁶ W
After reading this whole question, I feel like I've already
earned 5 points !
-- Two satellites at the same distance, different masses:
The forces of gravity between two objects are directly
proportional to the product of the objects' masses. In
other words, the gravitational forces between the Earth
and an object on its surface are proportional to the mass of
the object. In other words, people with more mass weigh more
on the Earth, and the Earth weighs more on them.
If the satellites are both at the same distance from Earth,
then the Earth pulls on the one with more mass with greater
force, and also the one with more mass pulls on the Earth
with greater force.
-- Two satellites with the same mass, at different distances:
The forces of gravity between two objects are inversely
proportional to the square of the distance between them.
In other words, the gravitational
forces between the Earth
and an object are inversely proportional
to the square of
the distance between the object and the center of the Earth.
If
the satellites both have the same mass, then the Earth
pulls on the nearer one with greater force, and also the
nearer one pulls on the Earth with greater force.
-- Resistor in a circuit when the voltage changes:
The resistance depends on how the resistor was manufactured.
Its resistance is marked on it, and doesn't change. It remains
the same whether the voltage changes, the current changes,
the time of day changes, the cost of oil changes, etc.
If you increase the voltage in the circuit where that resistor is
installed, the current through the resistor increases. If the current
remains constant, then you can be sure that somebody snuck over
to your circuit when you weren't looking, and they either installed
another resistor in series with the original one to make the total
resistance bigger, or else they snipped the original one out of the
circuit and quickly connected one with more resistance in its place.
