Magnetic Field and Electric Field Ranking Task

In summary, the problem involves a positively charged particle moving through a region with uniform electric and magnetic fields. The particle can have one of four velocities and the task is to rank them in increasing order of the amount of work the system would have to do on the particle to increase its speed by delta v. There is some confusion about the problem as it is not clearly defined, but based on the given information, it seems that the order would be W3>W2=W4>W1. The middle two may not be a tie as the particle's orbit continues and the directions of the forces change.
  • #1
jcfor3ver
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Homework Statement



First of all, the image for this problem is in an attachment (Jpeg), if you cannot view it let me know and I can change the format.

A positively charged particle moves through a region with uniform electric field pointing toward the top of the page and a uniform magnetic field pointing into the page. The particle can have one of the four velocities shown (initial speed is the same for all). Rank the four possibilities in order of increasing magnitude of the work (W1,W2,and W3) that the system would have to do on the particle to increase its speed by delta v (velocity final- velocity initial). Indicate ties where appropriate.


Homework Equations



F=qv+Bsintheta

Work=Force*distance

Right hand rule to determine direction of Force (if you do not know this, here's a link: http://physicsed.buffalostate.edu/SeatExpts/resource/rhr/rhr.htm )





The Attempt at a Solution




Here is my solution:

For v1: Force due to B and E field is in the positive y direction. Therefore to increase its speed by delta v would require the least amount of work. (since positive particle wants to move in direction of E field, a force due to the B-field in the same direction as the E field would require the least work?)


For v2: The force due to the B-field is perpendicular to the E-field, therefore the work required to cause the particle to speed up is equal to v4 (both are perpendicular to E)

For v3: The force due to B is opposite of the E-field, therefore my intuitive thought is that both forces are pushing against each other, resulting in the most Work that would have to be done by the system in order to increase the particles speed by delta v.

For v4: Same reasoning as v2.


Now those are my thoughts, I just am still confused on if my thinking is correct? My order would therefore be W3>W2=W4>W1
 

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  • #2
jcfor3ver said:

Homework Statement



First of all, the image for this problem is in an attachment (Jpeg), if you cannot view it let me know and I can change the format.

A positively charged particle moves through a region with uniform electric field pointing toward the top of the page and a uniform magnetic field pointing into the page. The particle can have one of the four velocities shown (initial speed is the same for all). Rank the four possibilities in order of increasing magnitude of the work (W1,W2,and W3) that the system would have to do on the particle to increase its speed by delta v (velocity final- velocity initial). Indicate ties where appropriate.


Homework Equations



F=qv+Bsintheta

Work=Force*distance

Right hand rule to determine direction of Force (if you do not know this, here's a link: http://physicsed.buffalostate.edu/SeatExpts/resource/rhr/rhr.htm )





The Attempt at a Solution




Here is my solution:

For v1: Force due to B and E field is in the positive y direction. Therefore to increase its speed by delta v would require the least amount of work. (since positive particle wants to move in direction of E field, a force due to the B-field in the same direction as the E field would require the least work?)


For v2: The force due to the B-field is perpendicular to the E-field, therefore the work required to cause the particle to speed up is equal to v4 (both are perpendicular to E)

For v3: The force due to B is opposite of the E-field, therefore my intuitive thought is that both forces are pushing against each other, resulting in the most Work that would have to be done by the system in order to increase the particles speed by delta v.

For v4: Same reasoning as v2.


Now those are my thoughts, I just am still confused on if my thinking is correct? My order would therefore be W3>W2=W4>W1

The problem is a bit confusing, so I think that's probably the reason nobody has tried to chime in. The question about how much work the system has to do on the particle to increase its velocity by delta-v seems very ill-defined. If you can modulate the E field with time, that changes things significatly. And increase the velocity over how much time? Over what fraction of an orbit, or how many orbits?

But given the problem statement, I think you are probably close to the right answer. However, I'm not sure the middle two are a tie, because as the particle's orbit continues from its current position (and velocity vector directions), one particle turns in the direction of E, and the other turns against it. Again, this goes to whether the problem is asking about an instantaneous amount of work for an instantaneous delta-v, or if they are asking over some portion of the initial orbit.

Hope that helps.
 

FAQ: Magnetic Field and Electric Field Ranking Task

1. What is the difference between a magnetic field and an electric field?

A magnetic field is a region in space where a magnetic force can be observed, while an electric field is a region in space where an electric force can be observed. The main difference between the two is that a magnetic field is created by moving charges or currents, whereas an electric field is created by stationary or fixed charges.

2. How are magnetic and electric fields related?

Magnetic and electric fields are related through Maxwell's equations, which state that a changing electric field will create a magnetic field, and a changing magnetic field will create an electric field. This relationship is known as electromagnetic induction and is the basis for many technologies such as generators and motors.

3. What is the unit of measurement for magnetic and electric fields?

The unit of measurement for magnetic fields is the tesla (T), named after Nikola Tesla. The unit of measurement for electric fields is the volt per meter (V/m).

4. How do magnetic and electric fields affect charged particles?

Magnetic fields can cause charged particles to experience a force called the Lorentz force, which can cause them to move in a circular or helical path. Electric fields, on the other hand, can cause charged particles to experience a force in the direction of the field. The combined effects of both fields play a crucial role in the behavior of charged particles in electric motors, generators, and other devices.

5. Can magnetic and electric fields be shielded or blocked?

Yes, both magnetic and electric fields can be shielded or blocked by certain materials. Magnetic fields can be shielded by high-permeability materials such as iron or steel, while electric fields can be blocked by conductive materials such as copper or aluminum. However, it is important to note that no material can completely block a magnetic or electric field, but they can reduce its strength.

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