Calculating Charge & Radius of a Van der Graaff Generator Dome

Click For Summary
SUMMARY

The maximum electrical potential of a Van der Graaff generator dome is 600 kV, with an electric field strength of 3.0 MV/m. To calculate the charge (q) and radius (r) of the dome, the equations E = kq/r² and V = kq/r are utilized. By substituting the known values into these equations, one can derive the necessary parameters for the dome's design. This approach ensures accurate calculations for both charge and radius based on the provided electrical specifications.

PREREQUISITES
  • Understanding of electrostatics, specifically electric potential and electric fields.
  • Familiarity with the equations E = kq/r² and V = kq/r.
  • Knowledge of the constants involved, such as Coulomb's constant (k).
  • Basic algebra skills for manipulating equations to solve for unknowns.
NEXT STEPS
  • Study the derivation and application of Coulomb's law in electrostatics.
  • Learn how to manipulate equations involving electric fields and potentials.
  • Explore practical applications of Van der Graaff generators in physics experiments.
  • Investigate safety measures and considerations when working with high-voltage equipment.
USEFUL FOR

Physics students, electrical engineers, and educators involved in teaching electrostatics and high-voltage systems will benefit from this discussion.

riincanavi1
Messages
3
Reaction score
0
1. A spherical dome of a Van der Graaff genenerator can be raised to a maximum electrical
potential of 600 kV; then additional charge leaks off in sparks as the electric field reaches 3.0
MV/m. Determine the charge and radius of the dome.



2. Homework Equations [E=kq/r^2 and V=kq/r]



3. I don't know how to relate the given Voltage and the given E field to find charge and radius
 
Physics news on Phys.org
You'll use the equations you quoted, for the values given in the problem statement.

I.e.,

3.0 MV/m = kq/r^2
600 kV = kq/r

Work with those to get r and q.
 

Similar threads

Van der Graaf Generator: Charge, Potential and Redesign Questions
  • · Replies 8 ·
Replies
8
Views
3K
Maximum electric field at the surface of a Van de Graaff generator
  • · Replies 2 ·
Replies
2
Views
2K
How to Calculate Force for Van de Graaff Generator | 70-Year Old Challenge
  • · Replies 7 ·
Replies
7
Views
4K
Find the Electric field at point p
  • · Replies 2 ·
Replies
2
Views
2K
What is the magnitude of the field at point R?
  • · Replies 5 ·
Replies
5
Views
2K
How Can I Improve My DIY Van de Graaff Generator to Prevent Charge Leakage?
  • · Replies 5 ·
Replies
5
Views
3K
What is the Speed and Number of Protons in a Van de Graaff Generator Beam?
  • · Replies 3 ·
Replies
3
Views
4K
Pressure versus stress in uniformly charged sphere
  • · Replies 11 ·
Replies
11
Views
2K
Electric field external to Conducting Hollow Sphere with charge inside
  • · Replies 23 ·
Replies
23
Views
5K
Van de Graaff generator questions?
  • · Replies 12 ·
Replies
12
Views
7K