A beam of electrons is deflected upward in a cathode ray tube
(
CRT
)
where the magnetic field points into the page.
(
a
)
Determine the direction of the electrons' initial velocity.
(
b
)
What would happen to the path of the beam if the magnetic field strength were doubled?
give the calculation step by step as like as full answer in 2 steps and explanation block in every steps.
And final answer summary
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don't use we, then,:.
Question:
A beam of electrons is deflected upward in a cathode ray tube
(
CRT
)
where the magnetic field points into the page.
(
a
)
Determine the direction of the electrons' initial velocity.
(
b
)
What would happen to the path of the beam if the magnetic field strength were doubled?
give the calculation step by step as like as full answer in 2 steps and explanation block in every steps.
And final answer summary
Definition of Parameters
Solutions are reviewed by our quality team mainly based on 6 parameters: Relevancy, Completeness, Accuracy, Clarity, Structure, and Voice.
Relevancy: This indicates how closely a solution aligns with the question asked. It evaluates whether the solution addresses the core aspects of the question and provides appropriate information.
Completeness: This indicates how thoroughly the solution addresses various asks in the question. It evaluates whether the solution has all essential information like calculations, diagrams, procedural steps, & explanatory statements in the solution.
Accuracy: It refers to how correct the provided solution is for the given question/s. This evaluates the correctness of the information/concept/method followed in the solution.
Clarity: Clarity refers to how easily the solution can be understood by the student. This evaluates the language complexity, readability, and redundancy of a solution.
Structure: Structure refers to how the solution is organized and presented in relation to the requirements of the question. This evaluates the necessity of steps and their effectiveness in helping the student grasp how to arrive at the solution.
Voice: This refers to the language and tone of the solution. This primarily evaluates whether a solution sounds human or overly non-human (bot-like).
don't use we, then,:.
This is AI generated Response.
Asked by: Maddamsetti jyothsna
Created at: 2025-05-31 23:05:31
Final Answer:
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**Definition of Parameters**
- **Relevancy:** The solution must directly address both parts of the question, using correct physical concepts about electron motion in magnetic fields.
- **Completeness:** The response should include explanations, step-by-step logic, and any necessary calculations, as well as a summary.
- **Accuracy:** All physical principles and calculations must be correct.
- **Clarity:** The answer should use clear language and logical steps.
- **Structure:** Steps should be numbered or clearly separated with explanations for each.
- **Voice:** The explanation should be in a human, instructive tone.
---
## (a) Determining the Direction of the Electrons' Initial Velocity
**Step 1: Use the Right-Hand Rule for Magnetic Force**
- The force experienced by a charged particle moving in a magnetic field is given by:
\[
\vec{F} = q (\vec{v} \times \vec{B})
\]
where:
- \( \vec{F} \) = force on the charge
- \( q \) = charge of the particle (for electron, \( q = -e \))
- \( \vec{v} \) = velocity of the particle
- \( \vec{B} \) = magnetic field vector
**Explanation:**
For an electron, the charge is negative. The direction of the force is found by applying the right-hand rule to \( \vec{v} \times \vec{B} \) and then reversing it (because electrons are negative).
---
**Step 2: Apply the Information from the Problem**
- The magnetic field (\( \vec{B} \)) points **into the page** (represented by '×').
- The electron beam is **deflected upward**.
To find the velocity direction:
1. Imagine a velocity vector \( \vec{v} \).
2. Point the fingers of the right hand in the direction of \( \vec{v} \).
3. Curl the fingers into the direction of \( \vec{B} \) (into the page).
4. The thumb points in the direction of the force for a **positive** charge.
5. Since electrons are negative, the force is opposite to the thumb.
For the force to be **upward** (toward the top of the page), the right-hand rule must give a force **downward** for a positive charge, so that the electron's force is upward.
- The velocity must be **to the right** (toward the right side of the page).
**Explanation:**
For velocity to the right and magnetic field into the page, the right-hand rule gives a force **downward** for a positive charge. For electrons (negative charge), the force is **upward**, matching the observed deflection.
---
## (b) Effect of Doubling the Magnetic Field Strength
**Step 1: Relationship Between Radius of Path and Magnetic Field**
- The radius of the circular path for a charged particle in a magnetic field is:
\[
r = \frac{mv}{|q|B}
\]
where:
- \( r \) = radius of curvature
- \( m \) = mass of electron
- \( v \) = speed of electron
- \( |q| \) = magnitude of charge (electron)
- \( B \) = magnetic field strength
**Explanation:**
The magnetic force provides the centripetal force that bends the electron's path into a circle.
---
**Step 2: Analyze the Effect of Doubling \( B \)**
- If \( B \) is doubled, \( r \) becomes:
\[
r' = \frac{mv}{|q|2B} = \frac{1}{2}\left(\frac{mv}{|q|B}\right) = \frac{r}{2}
\]
**Explanation:**
Doubling the magnetic field **halves the radius of the path**, causing the electron beam to bend more sharply.
---
## **Final Answer Summary**
**(a) The initial velocity of the electrons is directed to the right (toward the right side of the page).**
**(b) If the magnetic field strength were doubled, the radius of curvature of the electron beam’s path would be halved, so the beam would curve more sharply.**
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