Gauss' Law - Electric Flux and Electric Field

[Yuxtapuesto]

Homework Statement

A 2 C charge is spread uniformly in a hollow sphere with a radius of 50 cm.

a) What is the electric flux?

b) What is the magnitude and direction of an electric field 200 cm away?

Homework Equations

Electric flux = q/(permittivity of free space)

E = q/4(pi)(permittivity of free space)r²

q = charge
The permittivity of free space = 8.85 x 10^-12 C²/(N*m²)
r = radius

The Attempt at a Solution

Because the electric flux = the enclosed net charge divided by the permittivity of free space (approx. 8.85 x 10^-12) I attempted to use this equation. Using 2 C as the net charge, I found the answer to be about 2.26 N*m²/C

I had no idea how to solve the second part of the question, but referenced my book and found this equation:

E = q/4(pi)(permittivity of free space)r²

q = charge
The permittivity of free space = 8.85 x 10^-12 C²/(N*m²)
r = radius

My problem with this equation is that it doesn't seem to incorporate both the 50 cm and the 200 cm distances that are given within the question, but using 200 cm as the value of r, I calculated the answer to part b as 8.99 x 10⁹ N/C

Any help would be greatly appreciated!

 

[Thaakisfox]

The reason it doesn't incorporate the 50cm i.e. the radius of the sphere is that outside the sphere the electric field is the same as if you concentrated the charge spread throughout the sphere into a point charge at the center of the sphere.

This can be visualised easily by the first equation you gave. The one for the flux. (We are talking about a reference point outside of the sphere) You said that the flux is proportional to the enclosed net charge, hence if it was the flux of a point charge 2C you would get the same result, since the net charge enclosed is the same, as of the sphere.

 

[Yuxtapuesto]

Thank you. Can you / anyone possibly verify these answers?

 

[Thaakisfox]

What do you mean by verifying them? you theory is ok... You just have to substitute thenumerical values...

 

[Yuxtapuesto]

I mean that if someone could solve this problem independent of my work and share his or her answer with me, I would greatly appreciate it.

 

[Oyedeley2ky]

What is the formula for electric flux