Finding radius a of non-conducting spherical shell

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SUMMARY

The discussion focuses on calculating the radius of a non-conducting spherical shell given specific electrostatic potentials. The potential at the center is 200V, while at a distance of 50cm, it is 40V. The relationship between potential and distance is established through the equations V(0) = 200V and V(50) = 40V, leading to the conclusion that the radius can be determined by solving the equations C/r² = 200 and C/(r - 40)² = 40. By dividing these equations, the variable C can be eliminated, allowing for a straightforward calculation of the radius.

PREREQUISITES
  • Understanding of electrostatic potential and its relationship with distance.
  • Familiarity with the concept of non-conducting spherical shells in electrostatics.
  • Knowledge of algebraic manipulation to solve equations.
  • Basic principles of electrostatics, including the concept of constants in equations.
NEXT STEPS
  • Study the derivation of electrostatic potential for spherical charge distributions.
  • Learn about the properties of non-conducting materials in electrostatics.
  • Explore the concept of electric field and potential difference in spherical coordinates.
  • Practice solving similar problems involving electrostatic potentials and spherical shells.
USEFUL FOR

This discussion is beneficial for physics students, particularly those studying electrostatics, as well as educators seeking to clarify concepts related to electric potential in spherical charge distributions.

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Homework Statement



A non-conducting spherical shell is uniformly charged.
The electrostatic potential [itex]\phi[/itex] at the centre of the sphere is [itex]\phi[/itex]1 = 200V
The potential at distance r = 50cm from the centre is [itex]\phi[/itex]2 = 40V
Find the radius of sphere: a

Homework Equations



I seem to have missed this lecture.

The Attempt at a Solution



I understand that the potential (V) is a function of r (distance from centre) and satisfies:

V(0) = 200V
V(50) = 40V
V(a) = 0V

I've been reading up on this, but I can't seem to make sense out of this question. I can't seem to find a case for non conducting spherical shell. Would someone mind providing me a formula and clear steps to solve this problem?

Thank you!
 
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The "non-conducting" just means that you don't have to worry about the charge moving! Yes, V is a function of r- more specifically it is [itex]C/r^2[/itex].

So you have [itex]C/r^2= 200[/itex] and [itex]C/(r- 40)^2= 40[/itex], two equations you can solve for C and r.

Since you really only want to solve for r, I would recommending dividing one equation by another to eliminate C.
 
Thanks for the quick reply! I understand how to do the question now. is C just some constant? Or is it charge (Q)?

Not that it matters in this question but I'm certain I need to know this for other stuff.

Thanks again!
 

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