# Electric Field at Point P on Spherical Shell Insulator

• heartofaragorn
In summary, an insulator in the shape of a spherical shell is shown. The insulator is defined by an inner radius a = 4 cm and an outer radius b = 6 cm and carries a total charge of Q = +9 microC. Ey, the y-component of the electric field at point P which is located at (x, y) = (0, -5 cm) is 5.92085 e -08.
heartofaragorn

## Homework Statement

An insulator in the shape of a spherical shell is shown. The insulator is defined by an inner radius a = 4 cm and an outer radius b = 6 cm and carries a total charge of Q = +9 microC. You may assume that the charge is distributed uniformly throughout the volume of the insulator. What is Ey, the y-component of the electric field at point P which is located at (x, y) = (0, -5 cm)?

## Homework Equations

Volume of a sphere: 4/3pi R^3
Electric Field: E=4pi*r^2 = Qen / sigma o
Rho = total charge / total shell volume
Electric field at point P = rho * volume with charge

## The Attempt at a Solution

Consulted my physics prof on this, but I am still not getting the correct answer (is an interactive online problem that says "OK" or "NO"). He told me to calculate the volume of the sphere, which was .000637 due to the large hole in the middle (volume only applicable to an area between r = 4 cm and r = 6 cm). Calculated rho to be 0.014135 based upon a total charge of +9 micro Coulombs...is this where I'm going wrong? Based upon the answer I received for rho, I multiplied it by the volume of the area between 4 and 5 cm, which I thought was represented by the formula 4/3 pi r^3. That gave me an answer of 5.92085 e -08 for the electric field. There is no x-component and the point lies on the y-axis, so no angle is considered. I tried using both a positive and negative value and cannot get a happy little "OK". Where did I go wrong? Please help!

heartofaragorn said:
Electric field at point P = rho * volume with charge

I didn't understand this eqn.

[Based upon the answer I received for rho, I multiplied it by the volume of the area between 4 and 5 cm, which I thought was represented by the formula 4/3 pi r^3.

I presume you did 4/3 pi (5^3 -4^3) to get the volume?

Otherwise, your method looks all right.

I hadn't tried using 5^3 - 4^3, but when I did, I still didn't get the correct answer. The equation of E = rho * volume with charge was given to me by my professor.

I think you need to know more about electrostatics before solving this problem. Read up on the field of a point charge, the field of a uniformly charged shell -- inside and outside. Then, if you still don't get the answer, you can again post your question here. We'll be here.

How long will that take to do? Maybe just a couple of days.

Ok, I'll look more at the book and see what happens!

Received some help from a classmate...apparently when they wrote the online question, they messed around with the units...A LOT. Thanks for all the help, though!

I think we are in same physics 212 class. Can you finish explaining how the units were messed up? Because I'm pretty certain I have the right answer but it's not correct according to the system.

## What is a spherical shell insulator?

A spherical shell insulator is a type of insulation material that has a spherical shape and is used to prevent the flow of electricity through a conductor. It is typically made of a non-conductive material such as rubber, plastic, or glass.

## How does a spherical shell insulator work?

A spherical shell insulator works by creating a barrier between a conductor and its surroundings, preventing the flow of electrical current. The shape of the insulator also helps to distribute the electric field evenly, reducing the risk of electrical breakdown.

## What are the advantages of using a spherical shell insulator?

The main advantage of using a spherical shell insulator is its ability to provide insulation in all directions. It is also more efficient in distributing the electric field and can withstand higher voltages compared to other types of insulators.

## Where are spherical shell insulators commonly used?

Spherical shell insulators are commonly used in high voltage power lines, electrical transformers, and electronic devices. They are also used in laboratory equipment and scientific experiments involving high voltages.

## Can spherical shell insulators fail?

Yes, spherical shell insulators can fail if they are exposed to extremely high voltages or if they are damaged. This can lead to electrical breakdown and cause the flow of electricity. Regular maintenance and proper handling can help prevent failures in spherical shell insulators.

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