A particle of charge q and mass m is accelerated from rest through a potential difference V, after which it encounters a uniform magnetic field B. Follow below steps to find the radius of its circular orbit. Hint a. After being accelerated through potential difference V, what is the speed v of the charged particle? Hint for (a) V = (Give your answer in terms of given quantities above; be careful to distinguish V the voltage from v the speed. To enter ve (for example), type in "sqrt(e)"-or you may use exponent notation, "x^(1/2)" for x?.) b. Inside the region of magnetic field B, assuming the velocity v is perpendicular to the magnetic field B, what force does the charged particle experience? Hint for (b) The charged particle experiences force of magnitude (answer in terms of given variables), in the direction Select an answer c. The force you found in (b) above becomes the centripetal force for the charge as it undergoes a uniform circular motion. What is the radius of Curvature of th e circular motion?

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**Educational Content on Calculating the Radius of Circular Motion**

A particle of charge \( q \) and mass \( m \) is accelerated from rest through a potential difference \( V \), after which it encounters a uniform magnetic field \( B \). Follow the steps below to find the radius of its circular orbit.

### Part (a)

**Question:**
After being accelerated through a potential difference \( V \), what is the speed \( v \) of the charged particle?

**Hint for (a):**
Calculate the speed in terms of the given quantities. Distinguish \( V \) (the voltage) from \( v \) (the speed). You can enter \(\sqrt{e}\) as "sqrt(e)" or use exponent notation, "x^(1/2)" for \( x^{\frac{1}{2}} \).

**Answer Input:**
\[ v = \boxed{\text{(Enter expression here)}} \]

### Part (b)

**Question:**
Inside the region of the magnetic field \( B \), assuming the velocity \( \vec{v} \) is perpendicular to the magnetic field \( \vec{B} \), what force does the charged particle experience?

**Hint for (b):**
Consider the magnetic force acting on a charged particle.

**Answer Input:**
The charged particle experiences a force of magnitude
\[ \boxed{\text{(Enter expression here)}} \]
(answer in terms of given variables), in the direction
\[ \text{Select an answer (Use a dropdown menu)}. \]

### Part (c)

**Question:**
The force you found in (b) becomes the centripetal force for the charge as it undergoes uniform circular motion. What is the radius of curvature of the circular motion?

**Answer:** Calculate the radius using the balance between magnetic force and centripetal force.

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This content can be used in physics courses exploring electromagnetism and circular motion, helping students apply theoretical concepts to problem-solving scenarios.
Transcribed Image Text:**Educational Content on Calculating the Radius of Circular Motion** A particle of charge \( q \) and mass \( m \) is accelerated from rest through a potential difference \( V \), after which it encounters a uniform magnetic field \( B \). Follow the steps below to find the radius of its circular orbit. ### Part (a) **Question:** After being accelerated through a potential difference \( V \), what is the speed \( v \) of the charged particle? **Hint for (a):** Calculate the speed in terms of the given quantities. Distinguish \( V \) (the voltage) from \( v \) (the speed). You can enter \(\sqrt{e}\) as "sqrt(e)" or use exponent notation, "x^(1/2)" for \( x^{\frac{1}{2}} \). **Answer Input:** \[ v = \boxed{\text{(Enter expression here)}} \] ### Part (b) **Question:** Inside the region of the magnetic field \( B \), assuming the velocity \( \vec{v} \) is perpendicular to the magnetic field \( \vec{B} \), what force does the charged particle experience? **Hint for (b):** Consider the magnetic force acting on a charged particle. **Answer Input:** The charged particle experiences a force of magnitude \[ \boxed{\text{(Enter expression here)}} \] (answer in terms of given variables), in the direction \[ \text{Select an answer (Use a dropdown menu)}. \] ### Part (c) **Question:** The force you found in (b) becomes the centripetal force for the charge as it undergoes uniform circular motion. What is the radius of curvature of the circular motion? **Answer:** Calculate the radius using the balance between magnetic force and centripetal force. --- This content can be used in physics courses exploring electromagnetism and circular motion, helping students apply theoretical concepts to problem-solving scenarios.
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