Acceleration of Protons in Magnetic Field and Induced Electric Field

• cesaravila
In summary, in this scenario, there is a circular region with a uniform magnetic field and three protons held in place at different distances from the center. The magnetic field is shown to be a function of time in Figure 5(b). When the protons are released at t=3s, they will experience acceleration due to the force of the magnetic field and the induced electric field. The direction of acceleration is expected to be clockwise for the proton at the center and for the proton inside the field, and counterclockwise for the proton outside of the field. The magnitude of acceleration can be calculated using equations that relate the changing magnetic field to force and force to acceleration. Therefore, it is expected that all of the protons will experience
cesaravila
Inside of circular region of radius 10cm shown in Figure 5(a) there is
a uniform magnetic fi eld pointing upwards and three protons held in
place: one at the center, one at a distance of 5cm from the center and
one at a distance 15cm from the center e there is no magnetic field.
The magnetic fi eld as a function of time is shown in Figure 5(b). At
t = 3s the three protons are released.

- Which protons, if any, experience an acceleration? Justify your
response.
- What is the direction of acceleration for those protons expected to accelerate?
- What is the magnitude of acceleration for those protons expected to accelerate?
-Will any of the protons follow a circular path? If yes, how do you
know? If not, why not?

SEE ATTACHED FIGURES

My attempt at a solution:

I believe that all of the protons will accelerate either due to the force by the field or the force by the induced electric field.

As for direction I am unsure but think that the proton in the center will pivot about its axis in the clockwise while the other proton in the field has circular motion in the clockwise. The proton outside of the field will flow counterclockwise in circular motion.

I am unsure how to calculate the magnitude of acceleration.

I believe all of the protons will experience circular motion.

Attachments

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Are you ignoring the electric force of the protons on each other?
You should know an equation that relates the changing B field with the force on a charge, and another equation that relates the force to the acceleration.

1. What is the process of accelerating protons in a magnetic field and inducing an electric field?

The process of accelerating protons in a magnetic field and inducing an electric field is known as electromagnetic induction. This occurs when a moving charged particle, such as a proton, experiences a force from a magnetic field, causing it to accelerate and create an electric field in the process.

2. How does the strength of the magnetic field affect the acceleration of protons?

The strength of the magnetic field directly affects the acceleration of protons. The stronger the magnetic field, the greater the force on the protons and the faster they will accelerate. This is because the force on a charged particle in a magnetic field is directly proportional to the strength of the field.

3. What is the role of the induced electric field in the acceleration of protons?

The induced electric field plays a crucial role in the acceleration of protons. As the protons are accelerated by the magnetic field, they also create an electric field in the process. This induced electric field can further accelerate the protons, leading to a more powerful acceleration than just the magnetic field alone.

4. How do scientists control the acceleration of protons in a magnetic field?

Scientists can control the acceleration of protons in a magnetic field by adjusting the strength and direction of the magnetic field. By manipulating these variables, scientists can manipulate the force on the protons and thus control their acceleration.

5. What are the practical applications of accelerating protons in a magnetic field and inducing an electric field?

The acceleration of protons in a magnetic field and the resulting induced electric field have many practical applications. This phenomenon is used in particle accelerators to study the behavior of subatomic particles. It is also used in technologies such as MRI machines and particle beam therapy for cancer treatment.

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