# Electric potential at the outer surface of the insulating sphere?

• bodaciousbob
In summary: There is only 1 part to this problem.In summary, a solid insulating sphere of radius a = 3.6 cm, charged with a charge density ρ = -218.0 μC/m3, is fixed at the origin of a co-ordinate system. It is surrounded by an uncharged spherical conducting shell of inner radius b = 10.9 cm and outer radius c = 12.9 cm. The potential at the outer surface of the insulating sphere, V(a), can be calculated by starting at infinity and finding the potential at V(c), then V(b), and finally V(a). The potential difference between the outer surface of the conductor and the outer surface of
bodaciousbob
1.A solid insulating sphere of radius a = 3.6 cm is fixed at the origin of a co-ordinate system as shown. The sphere is uniformly charged with a charge density ρ = -218.0 μC/m3. Concentric with the sphere is an uncharged spherical conducting shell of inner radius b = 10.9 cm, and outer radius c = 12.9 cm.

http://imgur.com/R4vpBTr

1)
What is V(a), the electric potential at the outer surface of the insulating sphere? Define the potential to be zero at infinity.

2)
What is V(c) - V(a), the potentital differnece between the outer surface of the conductor and the outer surface of the insulator?

## Homework Equations

ΔV(a->b) = ∫E.dA3. I have so many miscellaneous pieces of paper scattered around my room, with chicken scratch on them, as I have been trying to many techniques for the last 3 hours. I just CAN'T get it - so I beg you - someone out there in internet land.. Can you PLEASE give me detailed instructions and walk me through this problem? There are 4 other parts to it, but by SOME miracle I have figured those out... Please??!

bodaciousbob said:
1.A solid insulating sphere of radius a = 3.6 cm is fixed at the origin of a co-ordinate system as shown. The sphere is uniformly charged with a charge density ρ = -218.0 μC/m3. Concentric with the sphere is an uncharged spherical conducting shell of inner radius b = 10.9 cm, and outer radius c = 12.9 cm.

http://imgur.com/R4vpBTr

1)
What is V(a), the electric potential at the outer surface of the insulating sphere? Define the potential to be zero at infinity.

2)
What is V(c) - V(a), the potential difference between the outer surface of the conductor and the outer surface of the insulator?

## Homework Equations

ΔV(a->b) = ∫E.dA

3. I have so many miscellaneous pieces of paper scattered around my room, with chicken scratch on them, as I have been trying to many techniques for the last 3 hours. I just CAN'T get it - so I beg you - someone out there in internet land.. Can you PLEASE give me detailed instructions and walk me through this problem? There are 4 other parts to it, but by SOME miracle I have figured those out... Please??!

Hello bodaciousbob. Welcome to PF !

Have you calculated the total charge on the insulating sphere?

What is the charge on the inner surface of the conducting spherical shell?

What is the charge on the outer surface of the conducting spherical shell?

Start at infinity and find the potential V(c), then V(b), and then V(a) .

#### Attachments

• R4vpBTr.jpg
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## What is electric potential at the outer surface of an insulating sphere?

The electric potential at the outer surface of an insulating sphere is the amount of electric potential energy per unit charge at that specific location on the sphere's surface. It is a measure of the electric potential difference between the surface of the sphere and a reference point, usually taken to be infinity.

## How is electric potential at the outer surface of an insulating sphere calculated?

The electric potential at the outer surface of an insulating sphere can be calculated by using the formula V = kQ/R, where V is the electric potential, k is the Coulomb's constant, Q is the charge of the sphere, and R is the radius of the sphere.

## Does the electric potential at the outer surface of an insulating sphere depend on the charge of the sphere?

Yes, the electric potential at the outer surface of an insulating sphere is directly proportional to the charge of the sphere. This means that as the charge of the sphere increases, the electric potential also increases.

## How does the radius of an insulating sphere affect the electric potential at its outer surface?

The electric potential at the outer surface of an insulating sphere is inversely proportional to the radius of the sphere. This means that as the radius of the sphere increases, the electric potential decreases, and vice versa.

## Can the electric potential at the outer surface of an insulating sphere be negative?

Yes, the electric potential at the outer surface of an insulating sphere can be negative. This occurs when the sphere has a negative charge, resulting in a negative electric potential. However, it is important to note that the absolute value of the electric potential is what matters, not its sign.

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