Answer:
The statement "if the magnetic force is always perpendicular to the velocity, the path of the particle is a straight line" is false.
Explanation:
The equation for the magnetic force on a charge q moving at velocity v on a magnetic field B is given by the (vectorial) Lorentz Force Law
From it we can clearly see that the <em>magnitude of the magnetic force </em>exerted on the particle is <em>proportional to the magnitude of the charge q and to the speed v of the particle</em>, and that it is also <em>perpendicular to the particle's velocity</em>. This means that at each instant it moves perpendicularly to the force, so <em>the work done by the magnetic force on the particle is zero</em>.
The statement "if the magnetic force is always perpendicular to the velocity, the path of the particle is a straight line" is false not only for this but for any force, a force always perpendicular to a velocity will curve the trajectory.
Answer:
The current is 2.0 A.
(A) is correct option.
Explanation:
Given that,
Length = 150 m
Radius = 0.15 mm
Current density
We need to calculate the current
Using formula of current density
Where, J = current density
A = area
I = current
Put the value into the formula
Hence, The current is 2.0 A.
Answer:
a)
b)
c)
d)
e)
Explanation:
1) Important concepts
Simple harmonic motion is defined as "the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law (F=-Kx). The motion experimented by the particle is sinusoidal in time and demonstrates a single resonant frequency".
2) Part a
The equation that describes the simple armonic motion is given by (1)
And taking the first and second derivate of the equation (1) we obtain the velocity and acceleration function respectively.
For the velocity:
(2)
For the acceleration
(3)
As we can see in equation (3) the acceleration would be maximum when the cosine term would be -1 and on this case:
Since we know the amplitude A=0.002m we can solve for like this:
And we with this value we can find the period with the following formula
3) Part b
From equation (2) we see that the maximum velocity occurs when the sine function is euqal to -1 and on this case we have that:
4) Part c
In order to find the total mechanical energy of the oscillator we can use this formula:
5) Part d
When we want to find the force from the 2nd Law of Newton we know that F=ma.
At the maximum displacement we know that X=A, and in order to that happens , and we also know that the maximum acceleration is given by::
So then we have that:
And since we have everything we can find the force
6) Part e
When the mass it's at the half of it's maximum displacement the term and on this case the acceleration would be given by;
And the force would be given by:
And replacing we have:
To solve this problem we will apply the concepts related to wavelength, as well as Rayleigh's Criterion or Optical resolution, the optical limit due to diffraction can be calculated empirically from the following relationship,
Here,
= Wavelength
d= Diameter of aperture
= Angular resolution or diffraction angle
Our values are given as,
The frequency of the sound is
The speed of the sound is
The wavelength of the sound is
Here,
v = Velocity of the wave
f = Frequency
Replacing,
The diffraction condition is then,
Replacing,
d = 0.24 m
Therefore the diameter should be 0.24m