# Non-uniform electric field and conducting spheres

• ifailatlife
And if it is not the final result, please explain what you are trying to calculate.In summary, the conversation involves determining electric field flux and electric field at various points in different scenarios. For Q1, a non-uniform electric field is given and the electric field flux is to be found through a rectangle in the xy plane. For Q2, a point charge is placed at the center of a non-conducting sphere with uniformly distributed charge, and the electric field at various points is to be found. The sphere is then replaced with a conducting hollow sphere and the electric field at various points is to be found again. There are also given equations for these calculations. However, there are some errors in the solutions provided and further explanation is
ifailatlife

## Homework Statement

Q1. A non-uniform electric field is given by the expression E=3yi+2zj-k.
Determine the electric field flux through a rectangle in the xy plane, extending from x=0 to x=20 cm and y=0 to y=15cm

Q2. A point charge q1 = +5nc is placed at the center of a non-conducting sphere (radius a=3) which has a chrage of Q= -8nc distributed uniformly throughout its volume. find:

a)the electric field at r=2m
b)the electric field for r=5m

If the non-conducting sphere is nw replaced with a conducting hollow sphere,having the same total charge, and the same radius. The cavity has a radius of 0.5m FIND:

C)The electric field at r=2m
D)The electric field at r=5m

## Homework Equations

Q1. ø=EAcosθ
Q2. Electricfield x area = Qenclosed/epsilon nod

## The Attempt at a Solution

http://i.imgur.com/ynihOMI.jpg
http://i.imgur.com/w7jTvvg.jpg

My attempts and the all the questions are in the links above

I would really appreciate some help on this PF.

Last edited:
ifailatlife said:

## Homework Statement

Q1. A non-uniform electric field is given by the expression E=3yi+2zj-k.
Determine the electric field flux through a rectangle in the xy plane, extending from x=0 to x=20 cm and y=0 to y=15cm

Q2. A point charge q1 = +5nc is placed at the center of a non-conducting sphere (radius a=3) which has a chrage of Q= -8nc distributed uniformly throughout its volume. find:

a)the electric field at r=2m
b)the electric field for r=5m

If the non-conducting sphere is nw replaced with a conducting hollow sphere,having the same total charge, and the same radius. The cavity has a radius of 0.5m FIND:

C)The electric field at r=2m
D)The electric field at r=5m

## Homework Equations

Q1. ø=EAcosθ
Q2. Electricfield x area = Qenclosed/epsilon nod

## The Attempt at a Solution

[ IMG]http://i.imgur.com/ynihOMI.jpg[/PLAIN]
[ IMG]http://i.imgur.com/w7jTvvg.jpg[/PLAIN]

My attempts and the all the questions are in the image

I would really appreciate some help on this PF.
Welcome to PF !

You need to post much smaller images than those !

I don't understand what you did at Q1. What is 3m? Where is your A, where did you calculate E*A?
Note that you can simply take the scalar product of the vectors, then the angle is included in the product and you don't have to calculate it.
As the field is not uniform, you might need an integral.

For the conducting sphere and r=2m: if the sphere is conducting, where is its charge?

mfb said:
I don't understand what you did at Q1. What is 3m? Where is your A, where did you calculate E*A?
Note that you can simply take the scalar product of the vectors, then the angle is included in the product and you don't have to calculate it.
As the field is not uniform, you might need an integral.

For the conducting sphere and r=2m: if the sphere is conducting, where is its charge?

Sorry
Area of the rectangle is 3m
Could you help me out with solving the integral ?

For the conducting hollow sphere Question C) at r=2m I tried it again and I think it should be Zero

ifailatlife said:
Sorry
Area of the rectangle is 3m
3m is a length, not an area. And there is at least one additional error in this result.

Could you help me out with solving the integral ?
Sure, just write down where you run into problems.

For the conducting hollow sphere Question C) at r=2m I tried it again and I think it should be Zero
If that is supposed to be the final result, don't forget the central charge.

## 1. What is a non-uniform electric field?

A non-uniform electric field is an electric field in which the strength and direction of the electric field changes at different points in space. This can be caused by the presence of charged objects or varying electric potentials.

## 2. How is a non-uniform electric field different from a uniform electric field?

A uniform electric field has a constant strength and direction at all points in space, while a non-uniform electric field varies in strength and direction. In a uniform electric field, the electric field lines are parallel and equidistant, while in a non-uniform electric field, the electric field lines are closer together in areas of higher field strength and farther apart in areas of lower field strength.

## 3. How are conducting spheres affected by a non-uniform electric field?

In a non-uniform electric field, conducting spheres will experience an electric force due to the difference in electric potential between different points on the sphere. This can cause the sphere to move or rotate, depending on the direction of the electric field and the shape of the sphere.

## 4. How is the electric field strength calculated in a non-uniform electric field?

The electric field strength in a non-uniform electric field can be calculated using the formula E = -∇V, where E is the electric field strength, ∇ is the gradient operator, and V is the electric potential. This formula takes into account the changing electric potential at different points in space.

## 5. How can a non-uniform electric field be visualized?

A non-uniform electric field can be visualized using electric field lines, which represent the direction and strength of the electric field at different points in space. These lines will be closer together in areas of higher field strength and farther apart in areas of lower field strength. Additionally, computer simulations and models can be used to visualize and understand the behavior of a non-uniform electric field.

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