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)