A particle with charge −− 5.90 nCnC is moving in a uniform magnetic field B⃗ =−(B→=−( 1.28 TT )k^k^. The magnetic force on the particle is measured to be F⃗ =−(F→=−( 3.70×10−7 NN )i^+()i^+( 7.60×10−7 NN )j^)j^.

(a) Calculate all the components of the velocity of the particle that you can from this information.
(b) Are there components of the velocity that are not determined by the measurement of the force? Explain.
(c) Calculate the scalar product v⃗ ⋅F⃗ . What is the angle between v⃗ and F⃗

The magnetic force and the scalar product allows to find the results for the questions about the movement of the particle in the field of magnetism are:

     a) The velocities are: vₓ = -100.6 m / s, = 49.0 m / s

     b) The z-axis component of velocity cannot be determined.

     c) Velocity and force are perpendicular.

Given parameters

To find

   a) The speeds

   b) there are components that cannot be determined

   c) The scalar product of v.F and the angle

The magnetic force is given by the vector product between the speed and the magnetic field.

     F = q v x B

Where the bold letters indicate vectors, F is the force, q the charge, v the velocity and B the magnetic field.

The best way to find forces is by solving the determinant.

a) Let's write the expression for the magnetic force.

let's write the components on each axis.

Let's calculate.

      -3.70 10⁻⁷ = 5.90 10⁻⁹  (-1.28)

      3.70 10² = 7.552  

      = 49.0 m / s

      7.60 10⁻⁷ = 5.90 10⁻⁹ vₓ (-1.28)

      7.60 10² = -7.552 vₓ

       vₓ =  

       vₓ = - 1.006 10²

       vₓ = -100.6 m / s

b) The component on the z axis cannot be determined from the given information since the vector product is zero

c) ask for the dot product and the angle between the vectors

          v. F = () . ( )

          v.F =    

          v .F = - 100.6 (-3.70 10⁻⁷) + 49.0 7.60 10⁻⁷

          v.F = -3.72 105 + 3.72 105

          v . F = 0

The scale product can be written

          v. F = |v| |F| cos θ        

          v. F = 0

Therefore, the cos θ = 0, this occurs for an angle of θ = 90º

Therefore the velocity and the forces are perpendicular.

In conclusion, using the magnetic force and the scalar product we can find the results for the questions about the movement of the particle in the field of magnetism are:

     a) The velocities are: vₓ = -100.6 m / s,  = 49.0 m / s

     b) The z-axis component of velocity cannot be determined.

     c) Velocity and force are perpendicular, the angle is: θ = 90º.

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Explanation:

Given that,

Charge q=-5.90nC

Magnetic field B= -1.28T k

And the magnetic force

F =−( 3.70×10−7N )i+( 7.60×10−7N )j

Let the velocity be V(xi + yj + zk)

Then, the force is given as

Note i×i=j×j×k×k=0

i×j=k. j×i=-k

j×k=i. k×j=-i

k×i=j. i×k=-j

The force in a magnetic field is given as

F= q(v×B)

−( 3.70×10−7N )i+( 7.60×10−7N )j =

q(xi + yj + zk) × -1.28k

−( 3.70×10−7N )i+( 7.60×10−7N )j=

q( -1.28x i×k - 1.28y j×k - 1.28z k×k)

−( 3.70×10−7N )i+( 7.60×10−7N )j=

q( 1.28xj - 1.28y i )

−( 3.70×10−7N )i+( 7.60×10−7N )j=

q( -1.28y i + 1.28x j)

So comparing comparing coefficients

let compare x axis component

-( 3.70×10−7N )i=-1.28qy i

−3.70×10−7N = -1.28qy

y= -3.7×10^-7/-1.28q

y= -3.7×10^-7/-1.28×-5.90×10^-9)

y=-48.99m/s

y≈-49m/s

Let compare y-axisaxis

7.6×10−7N j = 1.28qx j

7.6×10−7N = 1.28qx

x= 7.6×10^-7/1.28q

x= 7.6×10^-7/1.28×-5.90×10^-9

x=-100.64m/s

a. Then, the velocity of the x component is x= -100.64m/s

b. Also, the velocity component of the y axis is y=-49m/s

c. We will compute

V•F

V=-100.64i -49j

F=−( 3.70×10−7 N )i+( 7.60×10−7 N )j

Note

i.j=j.i=0. Also i.i = j.j =1

V•F is

(-100.64i-49j)•−(3.70×10−7N)i+(7.60×10−7 N )j =

3.724×10^-5 - 3.724×10^-5=0

V•F=0

d. Angle between V and F

V•F=|V||F|Cosx

0=|V||F|Cosx

Cosx=0

x= arccos(0)

x=90°

Since the dot product is zero, from vectors , if the dot product of two vectors is zero, then the vectors are perpendicular to each other

quantum mechanics or quantum physics is physics of very small objects (particles) and physical entities.

quantum physics has some parallels to our macro world and some pretty unique ideas which theoretically and mathematically proven to be true even though we will never be able to access them because of our size.

there are many types of particles: subatomic, elementary etc.

subatomic means they are smaller than atom, elementary means they are at the very basis of everything.

subatomic particles are for eg. protons, neutrons but not electrons.

elementary particles are categorised into 3 groups by what they do.

these 3 groups are quarks, leptons and bosons.

light for example is a particle more precisely a photon a part of leptons.

proton (subatomic particle) is made out of 2 up quarks and 1 down quark each of these has a fractional charge like . (i crazy)

most famous scientist who contributed to this physics are:

the topic itself us understand a lot and will probably be vastly used in the future (quantum computers, understanding the big bang,

we also must not forget quantum effects like:

and there is more. but probably too much for this answer to be consistent due to my average understanding of this topic.

hope this you understand quantum mechanics a little more. i'm not an expert in the topic (so don't be like wth if you are an expert) but i'm very interested in it.

anyways quantum physics is a very hard topic (harder than physics (perhaps)) therefore searching for every information there is about it and learning it is unfortunately impossible (you can only specialise into 1 - 3 things or more (perhaps

have fun and i wish you luck!

r3t40

im sorry i dont know