Equipotential surfaces; finding the radius

In summary, a metal sphere with a radius of 0.39 m and a charge of 0.55 μC needs to have equipotential surfaces drawn for 100-V intervals outside of the sphere. The radius of the first, tenth, and 100th equipotential from the surface can be determined by using the equation V = kQ/r, where V is the potential, k is the Coulomb's constant, Q is the charge, and r is the radius. The potential of the sphere itself should also be taken into consideration when calculating the radius.
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Homework Statement



a metal sphere of radius 0.39 m carries a charge 0.55 μC. Equipotential surfaces are to be drawn for 100-V intervals outside of the sphere.

Determine the radius of the first, tenth and 100th equipotential from the surface.


Homework Equations



V = kQ / r
Volt = (Coulombs Constant * Charge) / radius

The Attempt at a Solution



r = ((9.0X10^9 Nm²/C²)(.55X10^-6 C))/ (1 Nm/C)

r = ((9.0X10^9 Nm²/C²)(.55X10^-6 C))/ (10 Nm/C)

r = ((9.0X10^9 Nm²/C²)(.55X10^-6 C))/ (100 Nm/C)

all units cancel out and I'm left with meters but I'm getting the incorrect values according to the homework system that I'm using
 
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  • #2
Read the problem more carefully. The equipotential surfaces are 100 V apart.

What is the potential of the sphere itself? Start there.
 

Related to Equipotential surfaces; finding the radius

1. What are equipotential surfaces?

Equipotential surfaces are imaginary surfaces in a space where the potential remains constant at every point. In simpler terms, they are surfaces where the electric field is perpendicular to the surface at every point, meaning no work is required to move a charge along the surface.

2. How are equipotential surfaces related to electric fields?

Equipotential surfaces are closely related to electric fields because they are perpendicular to the electric field lines. This means that if a charge is placed on an equipotential surface, it will not experience any force due to the electric field.

3. How can I find the radius of an equipotential surface?

The radius of an equipotential surface can be found using the following equation: r = kQ/V, where r is the radius, k is the Coulomb's constant, Q is the charge, and V is the potential at the surface. This equation assumes a point charge at the center of the equipotential surface.

4. Can equipotential surfaces intersect?

Yes, equipotential surfaces can intersect. This happens when there are two or more point charges present, with each charge creating its own set of equipotential surfaces. The intersection of these surfaces indicates where the potential is the same due to the influence of multiple charges.

5. How can I visualize equipotential surfaces?

Equipotential surfaces can be visualized using field line diagrams or by plotting the potential values on a graph. In a field line diagram, the equipotential surfaces are represented by lines that are perpendicular to the electric field lines. On a graph, the equipotential surfaces are represented by curves that connect points with the same potential value.

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