Finding the Total Charge of a Non-Uniformly Charged Disc

[Hatyk]

Homework Statement

I have a disc with radius R. One half has the charge density of +2σ and the other half has −σ. The task is to find the total charge of the disc.

Homework Equations

dQ=ρ2πr^2 I would use this equation if the charge density was uniform

The Attempt at a Solution

My first idea was to split the disc in the middle and find the total charge of each part separately and then add them up. Thinking about it now, this solution feels wrong. What is the correct solution?

 

[alejandromeira]

Well, in my opinion the statement of problem not say if the half is the half of radius or the half of surface. My intuition says the half of surface, but you can make the two cases

 

[Chandra Prayaga]

Statement of the problem is not complete. Which two halves are we talking about?

 

[rude man]

Homework Statement

I have a disc with radius R. One half has the charge density of +2σ and the other half has −σ. The task is to find the total charge of the disc.

Homework Equations

dQ=ρ2πr^2 I would use this equation if the charge density was uniform

The Attempt at a Solution

My first idea was to split the disc in the middle and find the total charge of each part separately and then add them up. Thinking about it now, this solution feels wrong. What is the correct solution?

I see nothing wrong with your assumption. I'll go on a limb and say it doesn't matter if the charges are all +2s on one side and -s on the obverse side, vs. each side has half +2s and the other half -s.

 

[Chandra Prayaga]

How about half the radius with +2σ and the other half with -σ?

 

[gneill]

How about half the radius with +2σ and the other half with -σ?

Personally I'd have some difficulty justifying that given how the area of a disk varies with the radius