For elliptical obits: the direction of the velocity of the satellite is _______________________ (always, seldom, never) perpendi
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a)
(+x axis)
b)
(+x axis)
(+z axis)
c)
(+x axis)
(+y axis)
(-x axis)
Explanation:
a)
The electric force exerted on a charged particle is given by
where
q is the charge
E is the electric field
For a positive charge, the direction of the force is the same as the electric field.
In this problem:
is the charge
is the electric field, along the x-direction
So the electric force (along the x-direction) is:
towards positive x-direction.
The magnetic force instead is given by
where
q is the charge
v is the velocity of the charge
B is the magnetic field
is the angle between the directions of v and B
Here the charge is stationary: this means , therefore the magnetic force due to each component of the magnetic field is zero.
b)
In this case, the particle is moving along the +x axis.
The magnitude of the electric force does not depend on the speed: therefore, the electric force on the particle here is the same as in part a,
(towards positive x-direction)
Concerning the magnetic force, we have to analyze the two different fields:
- : this field is parallel to the velocity of the particle, which is moving along the +x axis. Therefore,
, so the force due to this field is zero.
: this field is perpendicular to the velocity of the particle, which is moving along the +x axis. Therefore,
. Therefore,
, so the force due to this field is:
where:
is the charge
is the velocity
is the magnetic field
Substituting,
And the direction of this force can be found using the right-hand rule:
- Index finger: direction of the velocity (+x axis)
- Middle finger: direction of the magnetic field (+y axis)
- Thumb: direction of the force (+z axis)
c)
As in part b), the electric force has not change, since it does not depend on the veocity of the particle:
(+x axis)
For the field , the velocity (+z axis) is now perpendicular to the magnetic field (+x axis), so the force is
And by substituting,
And by using the right-hand rule:
- Index finger: velocity (+z axis)
- Middle finger: magnetic field (+x axis)
- Thumb: force (+y axis)
For the field , the velocity (+z axis) is also perpendicular to the magnetic field (+y axis), so the force is
And by substituting,
And by using the right-hand rule:
- Index finger: velocity (+z axis)
- Middle finger: magnetic field (+y axis)
- Thumb: force (-y axis)
The time taken by the swimmer was 1 hour.
Why?
Since the swimmer is maintaining an angle of 150° while he was swimming, there were two components of the speed (horizontal and vertical). If we want to calculate the time taken by him to cross the river, we need to calculate the vertical speed and consider that the flow's speed is compensated by his horizontal speed.
We can calculate both components of the speed using the following formula:
Now, calculating we have:
Therefore, we have that the horizontal speed is compesating the flow's speed while his vertical speed is used to cross the river which is 1 Km wide.
Hence, we have that the tame taken is:
Have a nice day!