:-A :=B R A ring of radius R = 2.0 m has Q = -520 nC of charge uniformly distributed around it. A point charge q = +360 nC is held fixed at the center of the ring, as shown. An electron initially at A = 110.0 m is moving toward the ring along the ring's central axis. The electron momentarily stops at a point B = 6.0 m from the center of the ring before reversing direction. a) What is the potential difference VB – Va between z = 110.0 m and z = 6.0 m due to the ring and the point charge at the center of the ring? b) What was the initial speed of the electron at z = 110.0 m? Note: An expression for the electric potential at a distance of z on the axis of a uniformly charged ring of charge Q and radius R is given by V(2) =- ko
:-A :=B R A ring of radius R = 2.0 m has Q = -520 nC of charge uniformly distributed around it. A point charge q = +360 nC is held fixed at the center of the ring, as shown. An electron initially at A = 110.0 m is moving toward the ring along the ring's central axis. The electron momentarily stops at a point B = 6.0 m from the center of the ring before reversing direction. a) What is the potential difference VB – Va between z = 110.0 m and z = 6.0 m due to the ring and the point charge at the center of the ring? b) What was the initial speed of the electron at z = 110.0 m? Note: An expression for the electric potential at a distance of z on the axis of a uniformly charged ring of charge Q and radius R is given by V(2) =- ko
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Question
![A ring of radius \( R = 2.0 \, \text{m} \) has \( Q = -520 \, \text{nC} \) of charge uniformly distributed around it. A point charge \( q = +360 \, \text{nC} \) is held fixed at the center of the ring, as shown. An electron initially at \( A = 110.0 \, \text{m} \) is moving toward the ring along the ring’s central axis. The electron momentarily stops at a point \( B = 6.0 \, \text{m} \) from the center of the ring before reversing direction.
**Diagram Explanation:**
The diagram shows a vertical line labeled with the z-axis. The ring is depicted as a horizontal black circle centered on this axis, with a radius \( R \). A red "+" symbol inside the circle represents the point charge \( q \) at the center. The point along the z-axis at \( z = A \) is at the top of the diagram, and \( z = B \) is further down. The electron's path is marked from \( z = A \) to \( z = B \).
**Questions:**
a) What is the potential difference \( V_B - V_A \) between \( z = 110.0 \, \text{m} \) and \( z = 6.0 \, \text{m} \) due to the ring and the point charge at the center of the ring?
b) What was the initial speed of the electron at \( z = 110.0 \, \text{m} \)?
**Note:**
An expression for the electric potential at a distance \( z \) on the axis of a uniformly charged ring of charge \( Q \) and radius \( R \) is given by:
\[
V(z) = \frac{kQ}{\sqrt{R^2 + z^2}}
\]
Where:
- \( k \) is Coulomb's constant.
- \( V(z) \) is the electric potential at distance \( z \).
- \( R \) is the radius of the ring.
- \( Q \) is the charge on the ring.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e6b254a-d25d-479c-b42b-752b8b5bbcbb%2F3ec95570-7101-450f-8085-f6dc9620072e%2Fys5d77l_processed.png&w=3840&q=75)
Transcribed Image Text:A ring of radius \( R = 2.0 \, \text{m} \) has \( Q = -520 \, \text{nC} \) of charge uniformly distributed around it. A point charge \( q = +360 \, \text{nC} \) is held fixed at the center of the ring, as shown. An electron initially at \( A = 110.0 \, \text{m} \) is moving toward the ring along the ring’s central axis. The electron momentarily stops at a point \( B = 6.0 \, \text{m} \) from the center of the ring before reversing direction.
**Diagram Explanation:**
The diagram shows a vertical line labeled with the z-axis. The ring is depicted as a horizontal black circle centered on this axis, with a radius \( R \). A red "+" symbol inside the circle represents the point charge \( q \) at the center. The point along the z-axis at \( z = A \) is at the top of the diagram, and \( z = B \) is further down. The electron's path is marked from \( z = A \) to \( z = B \).
**Questions:**
a) What is the potential difference \( V_B - V_A \) between \( z = 110.0 \, \text{m} \) and \( z = 6.0 \, \text{m} \) due to the ring and the point charge at the center of the ring?
b) What was the initial speed of the electron at \( z = 110.0 \, \text{m} \)?
**Note:**
An expression for the electric potential at a distance \( z \) on the axis of a uniformly charged ring of charge \( Q \) and radius \( R \) is given by:
\[
V(z) = \frac{kQ}{\sqrt{R^2 + z^2}}
\]
Where:
- \( k \) is Coulomb's constant.
- \( V(z) \) is the electric potential at distance \( z \).
- \( R \) is the radius of the ring.
- \( Q \) is the charge on the ring.
Expert Solution
Step 1
Given:
The radius of the ring is R = 2 m
The magnitude of the charge distributed over the circular ring is Q = -520 nC
The magnitude of the point charge fixed at the center is q = 360 nC
The distance at which point A is situated in the z-axis A = 110 m
The distance at which point B is situated in the z-axis B = 6 m
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