Cross Product of Magnetic Field(B) and Velocity of Charged Particle(v).

[kripkrip420]

Homework Statement

Hi there. I am currently taking physics 30(algebra physics course) and we are in the electrostatics unit. I am curious as to why, when trying to find the force acting on a charged particle moving perpendicular to a magnetic field, the force results in a direction that is perpendicular to both velocity and magnetic field vectors and heads in the z-direction. This whole time, we have been dealing with vector addition or subtraction but now, we are multiplying vectors. I am just trying to understand, although it is not part of the curriculum, why the cross product of two vectors in the same dimensional space (x,y) results in a new vector that is now found in a dimensional space that the previous two vectors were never even a part of (x,y,z). Also, why are the vectors multiplied and not added. When I visualize the scenario in my head, I see a proton, for example, heading towards a magnetic field at a 90 degree angle. Normally, I would assume that the force would be in the same direction as the magnetic field. I assume this only because, when studying electric fields, the force acted in the same direction as the field.

Thank You for your help!

Homework Equations

The Attempt at a Solution

 

[cupid.callin]

the direction thing is (i guess) an experimental fact ... rest i don't know
as for the vector products it means that all the quantities should be necessarily not 0
like F = q vXB
if either of q,v,B is 0 ... force is 0
this will not be same if it was q + vXB or something like that

 

[kripkrip420]

the direction thing is (i guess) an experimental fact ... rest i don't know
as for the vector products it means that all the quantities should be necessarily not 0
like F = q vXB
if either of q,v,B is 0 ... force is 0
this will not be same if it was q + vXB or something like that

So your telling me that if I was to (hypothetically) place a proton or electron in a magnetic field, It would experience no force simply because its velocity is zero? That doesn't make sense to me. What could velocity possible have to do with the amount of force acting on a charged particle in a magnetic field? In other words, what is it about a particles motion that "creates" a force? Why doesn't the magnetic field exert a force on a charged object regardless of its velocity?

 

[cupid.callin]

So your telling me that if I was to (hypothetically) place a proton or electron in a magnetic field, It would experience no force simply because its velocity is zero?

Yes that's right.

What could velocity possible have to do with the amount of force acting on a charged particle in a magnetic field? In other words, what is it about a particles motion that "creates" a force? Why doesn't the magnetic field exert a force on a charged object regardless of its velocity?

always Remember that the laws of physics don't decide how things around will work. they are merely our explanations to the working of world. just in case magnetic force was q+vXB ... any moving particle won't experience the force.

and i said that i guess its experimental because my book gives me only that much explanations. Maybe there is some explanation but for that i guess we both have to wait for couple of years.

And did you ever ask yourself where does the law of gravitation comes from. you just think that Earth would fly off if there was no sun. that's because some of things are too obvious to predict that we agree to the rules explaining them as if we know where the rule came from.
(thats why Newton found it in 17th century )

And you said that why can't magnetic force be same as the electric force?
Do you know why electric force is the way it is? can't it be k(q +q)/r²
and moreover why two protons repel each other? or why even there are two charges and just not charge like mass
(as much as i have asked these kind of questions i guess no one knows answer to these)

 

[rwisz]

Hi there,

The cross product of two vectors, in this case the magnetic field (B) and the velocity of the charged particle (v), is a mathematical operation that results in a new vector that is perpendicular to both of the original vectors. This new vector, also known as the Lorentz force, is in the z-direction because it is the only direction that is perpendicular to both the x and y components of the original vectors.

In terms of why the cross product results in a new vector in a different dimensional space, it is because the cross product takes into account the direction of the vectors, not just their magnitude. When multiplying vectors, we are essentially finding the area of the parallelogram that is formed by the two vectors, which is a vector quantity. This is why the result is a new vector, as it takes into account both the magnitude and direction of the original vectors.

In terms of why the vectors are multiplied and not added, it is because the cross product operation is specifically designed to find the direction of the resulting force, rather than the magnitude. This is why the cross product is often used in situations involving motion in a magnetic field, as it allows us to determine the direction of the force acting on a charged particle.

I hope this explanation helps to clarify the concept of the cross product of magnetic field and velocity of a charged particle. Keep up the good work in your physics course!