Answer:
B). to the right
Explanation:
Since the direction of magnetic field is into the page
So here we know that
now the velocity is from bottom to top
so we have
now the force on the moving charge is given as
now we have
so force will be towards Right
Answer:
a)
b)
Step-by-step explanation.
In order to solve this problem, we mus start by plotting the given points and charges. That will help us visualize the problem better and determine the direction of the forces (see attached picture).
Once we drew the points, we can start calculating the forces:
which yields:
(I will assume the positions are in meters)
Next, we can make use of the force formula:
so we substitute the values:
which yields:
Now we can find its components:
And we can now write them together for the first force, so we get:
We continue with the next force. The procedure is the same so we get:
which yields:
Next, we can make use of the force formula:
which yields:
Now we can find its components:
And we can now write them together for the second, so we get:
We continue with the next force. The procedure is the same so we get:
which yields:
Next, we can make use of the force formula:
which yields:
Now we can find its components:
And we can now write them together for the third force, so we get:
So in order to find the resultant force, we need to add the forces together:
so we get:
So when adding the problem together we get that:
which is the answer to part a), now let's take a look at part b).
b)
Basically, we need to find the magnitude of the force and divide it into the test charge, so we get:
which yields:
and now we take the formula for the electric field which is:
so we go ahead and substitute:
Answer:
Among those two medium, light would travel faster in the one with a reflection angle of (when light enters from the air.)
Explanation:
Let denote the speed of light in the first medium. Let
denote the speed of light in the air. Assume that the light entered the boundary at an angle of
to the normal and exited with an angle of
. By Snell's Law, the sine of
and
would be proportional to the speed of light in the corresponding medium. In other words:
.
When light enters a boundary at the critical angle , total internal reflection would happen. It would appear as if the angle of refraction is now
. (in this case,
.)
Substitute this value into the Snell's Law equation:
.
Rearrange to obtain an expression for the speed of light in the first medium:
.
The speed of light in a medium (with the speed of light slower than that in the air) would be proportional to the critical angle at the boundary between this medium and the air.
For ,
is monotonically increasing with respect to
. In other words, for
in that range, the value of
increases as the value of
increases.
Therefore, compared to the medium in this question with , the medium with the larger critical angle
would have a larger
. such that light would travel faster in that medium.