Non-uniform electric field and conducting spheres

[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.

 

[SammyS]

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 !

 

[ifailatlife]

You need to post much smaller images than those !

Sorry
I'm fairly new to this forum so I don't know how to edit posts.
Here:
http://i.imgur.com/ynihOMI.jpg
http://i.imgur.com/w7jTvvg.jpg

EDIT: nvm found it

 

[mfb]

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?

 

[ifailatlife]

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

 

[mfb]

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.