Answer:
First, let's define the coordinate axes: positive x direction is to the right, positive y direction is to upwards, and z direction is out-of-the plane (towards you).
If the particle is moving with velocity
in the presence of an external E-field, than according to the below formula E-field pushes the positive charge in the direction of the field, which is upward.
.
If the velocity of the particle is unchanged, this means that the particle does not have an acceleration, so net force applied to the particle is zero.
We know that the force caused by the E-field is upwards, so an equal amount of another force is directed downwards. This second force is caused by magnetic field. ![|F_B| = qvB](https://tex.z-dn.net/?f=%7CF_B%7C%20%3D%20qvB)
![F_{net} = 0\\F_{net} = F_E - F_B\\0 = qE_0 - qvB\\qE_0 = qvB\\B = \frac{E_0}{v}](https://tex.z-dn.net/?f=F_%7Bnet%7D%20%3D%200%5C%5CF_%7Bnet%7D%20%3D%20F_E%20-%20F_B%5C%5C0%20%3D%20qE_0%20-%20qvB%5C%5CqE_0%20%3D%20qvB%5C%5CB%20%3D%20%5Cfrac%7BE_0%7D%7Bv%7D)
This is the magnitude of the magnetic field.
For the direction of the magnetic field we can use right-hand rule with the following equation:
![F_B = q(v \times B)](https://tex.z-dn.net/?f=F_B%20%3D%20q%28v%20%5Ctimes%20B%29)
Here,
is in the x-direction.
is in the (-y)-direction.
According to the right-hand rule, B-field should be in the z-direction (out-of-the plane, towards you.)
Explanation:
Total distance traveled = 74 + 83 = 157 km.
Total time traveled = 1 + 5 = 6 hours.
Average speed = total distance / total time
Average speed = 157 km / 6 hours = 26.1666 km per hour.
Round the answer as needed.
Answer:
Gravitational force is directly proportional to the distance between objects.
The energy of a single photon is given by:
![E=hf](https://tex.z-dn.net/?f=E%3Dhf)
where
E is the energy
h is the Planck constant
f is the frequency of the light
The light in our problem has a frequency
![f=5.49 \cdot 10^{14}Hz](https://tex.z-dn.net/?f=f%3D5.49%20%5Ccdot%2010%5E%7B14%7DHz)
, so the energy of each photon of that light is:
(a) We must first look at the formulas of the velocities of each toy car. v1 =
-4.2 + 2.60t. v2 = 5.20. When the two cars have equal speed, then
v1 = v2
-4.2 + 2.60t = 5.20
2.60t = 9.40
t = 3.62 s
(b) Their speed would then be 5.20 m/s. The toy car does not change speed since it doest not have any acceleration.
(c) The two cars will pass each other when their positions are equal.
x1 = 13.5 - 4.2t + 0.5*2.60t^2
x2 = 8.5 + 5.20t
x1 = x2
13.5 - 4.2t + 1.30t^2 = 8.5 + 5.20t
1.30t^2 - 9.40t + 5.0 = 0
t = 6.65s or t = 0.58 s
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