Nullifying Lorentz Force on Proton Moving in Parallel Direction

In summary, the electric field must be applied in the region ##-i+k## to ##i-k##, so that the Lorentz force is zero.
  • #1
Celso
33
1

Homework Statement


A proton moves with a speed ##v = 3 \cdot 10^5 \frac{m}{s}## in the parallel direction to ##i+k##. A magnetic field of ##1T##, in the ##i+j+k## acts over it. Which electric field must we apply in this region so that the Lorentz force over the proton is null?

Homework Equations


##F = q(\vec{E} + \vec{v}\times\vec{B})##

The Attempt at a Solution


My first step (and the wrong one) was consider ##\vec{v} = 3\cdot10^5 (i+k)##, then I made the vectorial product ##\vec{v}\times\vec{B}## finding ##3\cdot10^5(-i+k)##, then I simply wanted to find the electric field vector such as ##\vec{E} + 3\cdot 10^5 (-i+k) = \vec{0} \rightarrow \vec{E} = 3\cdot 10^5(i-k)##

My doubt is: how do I represent the velocity vector in this case by knowing its size and which vector it is parallel to?
 
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  • #2
Celso said:

Homework Statement


A proton moves with a speed ##v = 3 \cdot 10^5 \frac{m}{s}## in the parallel direction to ##i+k##. A magnetic field of ##1T##, in the ##i+j+k## acts over it. Which electric field must we apply in this region so that the Lorentz force over the proton is null?

Homework Equations


##F = q(\vec{E} + \vec{v}\times\vec{B})##

The Attempt at a Solution


My first step (and the wrong one) was consider ##\vec{v} = 3\cdot10^5 (i+k)##, then I made the vectorial product ##\vec{v}\times\vec{B}## finding ##3\cdot10^5(-i+k)##, then I simply wanted to find the electric field vector such as ##\vec{E} + 3\cdot 10^5 (-i+k) = \vec{0} \rightarrow \vec{E} = 3\cdot 10^5(i-k)##

My doubt is: how do I represent the velocity vector in this case by knowing its size and which vector it is parallel to?
Maybe you should consider to make calculations with unit vectors. For example, the unit vector in ##i+k## direction would be ##(i+k)/\sqrt {2}## so now you can multiply it with ##v##. And you can do this for the magnetic field.
 
  • #3
I find it convenient to represent such things as column vectors with unit values as entries. So in your case:

upload_2018-10-27_12-7-0.png


Then when it comes time to do the vector math, the cross product becomes trivial as the constants can all be "moved out of the way" leaving two very simple vectors to multiply.
 

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1. What is the Lorentz Force?

The Lorentz Force is the force experienced by a charged particle moving in an electric and magnetic field. It is given by the equation F = q(E + v x B), where q is the charge of the particle, E is the electric field, v is the velocity of the particle, and B is the magnetic field.

2. Why is it important to nullify the Lorentz Force on a proton?

Nullifying the Lorentz Force on a proton is important because it allows the proton to move in a straight line without any deflection. This is particularly useful in particle accelerators where precise control of the proton's trajectory is necessary for experiments.

3. What is the parallel direction in relation to the Lorentz Force?

The parallel direction refers to the direction of the proton's motion in relation to the electric and magnetic fields. When the proton is moving parallel to the electric and magnetic fields, the Lorentz Force is at its maximum and needs to be nullified.

4. How can the Lorentz Force be nullified on a proton moving in parallel direction?

There are a few ways to nullify the Lorentz Force on a proton moving in parallel direction. One way is to adjust the strength and direction of the electric and magnetic fields so that they cancel out the force. Another way is to use a technique called beam focusing, which uses alternating electric and magnetic fields to keep the proton on a straight path.

5. What are the applications of nullifying the Lorentz Force on a proton?

Nullifying the Lorentz Force on a proton has many applications, including in particle accelerators, nuclear reactors, and medical imaging. It also allows for the study of subatomic particles and their interactions, leading to a better understanding of the fundamental laws of nature.

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