Part a) The connection between the electric field and the magnetic field in an electromagnetic wave is
where
E signifies the strength of the electric field
B indicates the strength of the magnetic field
c represents the speed of light
Using the equation, we determine:
Part b) The text does not clarify the orientation of the magnetic field on the y-axis: I speculate it points in the y+ direction.
The direction of the electric field can be established using the right-hand rule, which states:
- the index finger shows the direction of E
- the middle finger indicates the orientation of B
- the thumb reveals the propagation direction of the wave
Because the wave propagates in the x+ direction, and the magnetic field in the y+ direction, we conclude that the electric field direction (index finger) must be z-.
Velocity = 71 meters per minute (MPM)
S stands for Speed
D means Distance
T represents Time
To calculate Speed, divide Distance by Time.
J(r) = Br. We know that the area of a small segment, dA, is represented as 2 π dr. Thus, I = J A and dI = J dA. Plugging in the values gives us dI = B r. 2 π dr which simplifies to dI= 2π Br² dr. Now, integrating the above equation: Given that B= 2.35 x 10⁵ A/m³, with r₁ = 2 mm and r₂ equal to 2 + 0.0115 mm, or 2.0115 mm.
Answer:
a. Angle= 28.82°
b. Approved. Although he might feel cold, he should be able to cross.
Explanation:
Velocity Vector
Velocity is a measure of how quickly something is moving in a specific direction. It is represented as a vector that has both magnitude and direction. If an object can only move in one direction, then speed can serve as the scalar equivalent of that velocity (only focusing on magnitude).
a.
The explorer aims to swim across a river to reach his campsite, as depicted in the image below. The river's velocity is vr and the explorer's swimming speed in still water is ve. If he were to swim straight towards the campsite, he would end up downstream due to the river's current. Therefore, he must swim at an angle that allows him to overcome the current while still moving towards his goal. This angle relative to the shore is what we need to determine. The explorer's speed can be broken down into its horizontal (vx) and vertical (vy) components. In order to counteract the river's flow:
We can calculate the vertical component of the explorer's swimming speed as
Thus
Finding the value of 
Then the angle is given by
b.
The component of the explorer's velocity that goes horizontally is
This represents the actual velocity directed towards the campsite
Considering that
To find t
Calculating the duration for the explorer to cross the river
As this time is under the hypothermia threshold (300 seconds), the conclusion is
Approved. Although he will feel cold, he should manage to cross successfully.
Answer:
Part a)
A = 0.0581 m
Part b)
T = 0.37 s
Explanation:
A slice is dropped onto the plate from a height of 0.250 m,
therefore the speed of the slice upon impact is calculated as
We know that
Now applying the conservation of momentum:
From this equation, we find:
When the slice rests on the plate, the new mean position can be expressed as
We also determine that the speed of SHM is represented as
Here, we derive values from
Using the previous formula gives:
Part b)
The time period for the scale is computed as
