Work to Construct Conducting Spheres

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SUMMARY

The discussion focuses on calculating the work required to construct two conducting spheres: one with radius 'a' and charge '+q', and another with radius 'b' and charge '-q'. The initial potential energy is zero since the charges are infinitely far away. The work done to assemble the first sphere is determined by calculating its potential energy at radius 'a'. The challenge arises in accounting for the interaction between the two spheres during the construction of the second sphere.

PREREQUISITES
  • Understanding of electrostatics, specifically Coulomb's Law (F=ke(q_1)(q_2)/r^2)
  • Knowledge of electric field calculations (E=ke(integral(dq/r^2)))
  • Familiarity with potential energy concepts in electrostatics (U=integral(F))
  • Ability to apply work-energy principles (W=delta(U))
NEXT STEPS
  • Calculate the potential energy of a conducting sphere using U_a at radius 'a'
  • Explore the effects of charge distribution on the potential energy of multiple conductors
  • Investigate the concept of electric field interactions between charged spheres
  • Learn about the method of images in electrostatics for simplifying complex charge configurations
USEFUL FOR

Students and educators in physics, particularly those studying electrostatics, as well as anyone interested in understanding the principles of charge interactions and energy calculations in conducting materials.

Ferbs207
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1. Homework Statement

How much work does it take to construct a conducting sphere of radius 'a' and charge '+q' by pulling charges ('dq') from an infinite distance? Then construct another conducting sphere of radius 'b' and charge '-q' around the sphere of radius 'a'. Given 'a'<'b'.

2. Homework Equations
F=ke(q_1)(q_2)/r^2
E=ke(integral(dq/r^2)
U=integral(F)=1/q(integral(E))
W=delta(U)

3. The Attempt at a Solution

If the charges are initially infinitely far, then the initial potential energy is 0. This means that all I need to do is calculate the potential energy of the sphere at radius 'a', which will be my value for work. Let's say the potential energy at radius 'a' is U_a.

It's the second part of the question that I find difficult. How do I account for the interactions between the two conducting sphere when constructing the second one around it?
 
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Hi Ferbs207 and welcome to PF. Please follow the rules of this forum and use the template when you seek help with homework. Show us the relevant equations and tell us what you tried and what you think about the problem. We just don't give answers away.
 

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