**Title:** Electric Potential of a Hollow ConeA thin-walled, insulating hollow cone has a uniform surface charge and a total charge of \( Q \). The height and radius of the cone are equal. The electric potential from the cone is zero at a point far from the apex, and at the apex, the electric potential is given by the equation:\[ V = \frac{\sqrt{2}kQ}{h} \]where \( k \) is Coulomb’s constant, \( Q \) is the total charge, and \( h \) is the height (also the radius in this problem).**Problems:**a. If \( h = 5.00 \, \text{cm} \) and \( Q = +10.0 \, \text{nC} \), what is the speed of an electron when it hits the apex of the cone if released from rest far from the cone?b. Prove the electric potential is equal to \( V = \frac{\sqrt{2}kQ}{h} \). Hint: Think of the cone as a sum of an infinite number of rings starting at the apex. Each ring has a bigger radius and is farther away from the apex by the same amount as the radius. Start with the potential for a ring and add up an infinite number of rings. The surface area of the sloped part of the cone (not the circular base) is \( A = \pi r \sqrt{h^2 + r^2} \). Setting it up is worth a lot of partial credit.**Diagram Description:**The diagram shows a right circular cone with:- Apex at the top- Radius \( R = h \)- Height \( h = R \)- Annotated with distance \( h \) from apex to base along the side- An electron (\( e^- \)) approaching the apex of the coneThis content is part of a lesson on electric potential and involves calculations and conceptual understanding of electric fields and potential due to charged surfaces.

The speed of the electron when it hits the apex of the cone is given by The height of the cone h=5cm…

A thin walled, insulating, hollow cone has a uniform surface charge, and total charge of Q. The height and radius of the cone are equal. The electric potential far from the cone is zero and at the apex electric potential is given by the equation VZkQ h V = where k is Coulomb's constant, Q is the total charge, and h is the height (also the radius in this problem) a. If h=5.00cm and Q is +10.0nC, what is the speed of an electron when it hits the apex of the cone when released from rest far from the cone? √ZkQ Hint: think of the cone b. Prove the electric potential is equal to V = as a sum of an infinite number of rings starting the apex. Each ring has bigger radius and is farther away from the apex by the same as the radius. Start with the potential for a ring and add up an infinite number of rings. The surface area of the sloped part of the cone (not the circular base) is A = πr√/h² +² Setting it up is worth a lot of partial credit. Apex R=h h=R

A thin walled, insulating, hollow cone has a uniform surface charge, and total charge of Q. The height and radius of the cone are equal. The electric potential far from the cone is zero and at the apex electric potential is given by the equation VZkQ h V = where k is Coulomb's constant, Q is the total charge, and h is the height (also the radius in this problem) a. If h=5.00cm and Q is +10.0nC, what is the speed of an electron when it hits the apex of the cone when released from rest far from the cone? √ZkQ Hint: think of the cone b. Prove the electric potential is equal to V = as a sum of an infinite number of rings starting the apex. Each ring has bigger radius and is farther away from the apex by the same as the radius. Start with the potential for a ring and add up an infinite number of rings. The surface area of the sloped part of the cone (not the circular base) is A = πr√/h² +² Setting it up is worth a lot of partial credit. Apex R=h h=R

College Physics

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

**Title:** Electric Potential of a Hollow Cone

A thin-walled, insulating hollow cone has a uniform surface charge and a total charge of \( Q \). The height and radius of the cone are equal. The electric potential from the cone is zero at a point far from the apex, and at the apex, the electric potential is given by the equation:

\[ V = \frac{\sqrt{2}kQ}{h} \]

where \( k \) is Coulomb’s constant, \( Q \) is the total charge, and \( h \) is the height (also the radius in this problem).

**Problems:**

a. If \( h = 5.00 \, \text{cm} \) and \( Q = +10.0 \, \text{nC} \), what is the speed of an electron when it hits the apex of the cone if released from rest far from the cone?

b. Prove the electric potential is equal to \( V = \frac{\sqrt{2}kQ}{h} \). Hint: Think of the cone as a sum of an infinite number of rings starting at the apex. Each ring has a bigger radius and is farther away from the apex by the same amount as the radius. Start with the potential for a ring and add up an infinite number of rings. The surface area of the sloped part of the cone (not the circular base) is \( A = \pi r \sqrt{h^2 + r^2} \). Setting it up is worth a lot of partial credit.

**Diagram Description:**

The diagram shows a right circular cone with:
- Apex at the top
- Radius \( R = h \)
- Height \( h = R \)
- Annotated with distance \( h \) from apex to base along the side
- An electron (\( e^- \)) approaching the apex of the cone

This content is part of a lesson on electric potential and involves calculations and conceptual understanding of electric fields and potential due to charged surfaces.

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