Finding potential difference between two points on a cone

In summary, the conversation is about solving a problem from the book "Intro to EM" by David Griffiths and comparing the solutions with the instructor's solution manual. The problem involves using cylindrical coordinates and finding the distance of an area element from the origin. The use of LateX is also discussed as a tool for writing equations.
  • #1
issacnewton
1,000
29
Hello

I am solving some problems from "Intro to EM" by David Griffiths ( third edition)
Problem 2.26 ( attached file 2.26.jpg) and I have also attached the solution from the solution
manual (griffiths-2.26.jpg). For both part a and b I am getting different answer.

I have chosen vertex as the origin and the axis of the cone as the positive z-axis.
The bottom of the cone is toward positive z axis. Now any differential area element on the cone would be (using cylindrical coordinates) , x*d(phi)*dz , where x is the perpendicular
distance of the area element from the z-axis. But for this geometry, x=z for any point on the
cone , so dz = dx. The distance r of this area element from the origin(vertex) would be
sqrt(2)*x. I am supposed to use the formula (formula.jpg).

Why are my solutions not working ? Or is the instructor's solution manual incorrect ?

Regards
I Newton
 

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  • #2
Hello IssacNewton! :smile:

I can see the instructor's solution but not your solution. :confused:
 
  • #3
hello tiny-tim

i will write my solution though i just explained what i did. i see people here write using LateX. how can i write like that ? is there any 'How to' tutorial for doing that ?

Newton
 
  • #4
Hello IssacNewton! :smile:

(just got up :zzz: …)

LaTeX is very easy.

The best way to see how to use it is click the "QUOTE" button on someone else's post and copy what they do. :wink:

There's a list of symbols and a guide at http://www.physics.udel.edu/~dubois/lshort2e/node61.html#SECTION008100000000000000000"

and there's also a palette of symbols if you click the ∑ tag just above the Reply box (though I never use it).
 
Last edited by a moderator:

1. How do you calculate the potential difference between two points on a cone?

The potential difference between two points on a cone can be calculated by subtracting the potential at one point from the potential at the other point. This can be represented by the equation V = V2 - V1, where V2 is the potential at the second point and V1 is the potential at the first point.

2. What factors affect the potential difference on a cone?

The potential difference on a cone is affected by the distance between the two points, the shape and size of the cone, and the charge distribution on the cone. The potential difference may also be affected by external factors such as the presence of other charged objects nearby.

3. Can the potential difference on a cone be negative?

Yes, the potential difference on a cone can be negative. This indicates that the potential at the first point is greater than the potential at the second point. However, it is important to note that the absolute value of the potential difference is what is typically used in calculations.

4. How does the potential difference on a cone relate to electric field?

The potential difference on a cone is directly related to the electric field. The electric field is the rate of change of potential with respect to distance, meaning that a larger potential difference between two points will result in a stronger electric field.

5. Is the potential difference the same at all points on a cone?

No, the potential difference is not the same at all points on a cone. The potential difference will vary depending on the distance from the two points and the shape of the cone. Additionally, if there are any other charged objects nearby, this can also affect the potential difference at different points on the cone.

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