Radii of eqiuipotential surfaces of a charged metal sphere

Click For Summary
SUMMARY

The discussion focuses on calculating the radii of equipotential surfaces for a charged metal sphere with a radius of 0.29 m and a charge of 0.90 µC. The relevant equation used is V = kQ/r, where k is Coulomb's constant (8.99 x 10^9 NM²/C²). The potential at the surface of the sphere is calculated to be approximately 27931.03 V. To find the radii for the first, tenth, and hundredth equipotential surfaces, the potential values must be adjusted accordingly, but initial attempts at calculating these values were incorrect due to misunderstanding the relationship between the sphere's radius and the equipotential surfaces.

PREREQUISITES
  • Understanding of electrostatics and electric potential
  • Familiarity with Coulomb's law and the constant k (8.99 x 10^9 NM²/C²)
  • Ability to manipulate algebraic equations
  • Knowledge of equipotential surfaces in electrostatics
NEXT STEPS
  • Learn how to calculate electric potential for different charge distributions
  • Study the concept of equipotential surfaces in greater detail
  • Explore the implications of radius in electric potential calculations
  • Investigate the relationship between potential difference and distance in electrostatics
USEFUL FOR

Students studying electrostatics, physics educators, and anyone involved in solving problems related to electric potential and charged objects.

RoosterCancer
Messages
3
Reaction score
0

Homework Statement



A metal sphere of radius r0 = 0.29 m carries a charge Q = 0.90 µC. Equipotential surfaces are to be drawn for 100 V intervals outside the sphere. Determine the radius r of the following equipotentials from the surface.
a) first:___m
b) tenth:___m
c) 100th:_____m


Homework Equations



V=kQ/r --> r=kQ/V



The Attempt at a Solution



I've tried plugging the numbers from the problem in the equation:

r=(8.99 x 10^9 NM^2/C^2)*(0.9 x 10^-6 C)/(100V) = 80.91m

and it's incorrect. I assume the radius of the sphere itself comes into play, but I'm not sure where. Can anyone help?
 
Physics news on Phys.org
RoosterCancer said:

Homework Statement



A metal sphere of radius r0 = 0.29 m carries a charge Q = 0.90 µC. Equipotential surfaces are to be drawn for 100 V intervals outside the sphere. Determine the radius r of the following equipotentials from the surface.
a) first:___m
b) tenth:___m
c) 100th:_____m

Homework Equations



V=kQ/r --> r=kQ/V

The Attempt at a Solution



I've tried plugging the numbers from the problem in the equation:

r=(8.99 x 10^9 NM^2/C^2)*(0.9 x 10^-6 C)/(100V) = 80.91m

and it's incorrect. I assume the radius of the sphere itself comes into play, but I'm not sure where. Can anyone help?
What is the potential at the surface of the ball ?
 
I was able to find the potential of the ball:

V=(9 x10^9NM^2/C^2)*(0.9 x10^-6 C)/0.29m = 27931.03V

and was able to answer part a, by adding 100 V to the ball's potential and using the formula. So, for b, I added 1000 V to the potential and for c I added 10000 V to the potential, but the results were incorrect.
 

Similar threads

Replies
5
Views
1K
Replies
23
Views
5K
Replies
21
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 14 ·
Replies
14
Views
3K
Replies
5
Views
4K
Replies
2
Views
2K
Replies
6
Views
2K