- #1

tellmesomething

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- Homework Statement
- Theres a hollow sphere whose ## \sigma ## = ## \sigma_0 cos \theta ## where ##\theta ## is the polar angle/THE angle made with the x axis. Find field inside shell.

- Relevant Equations
- Expression of electric field on axis due to a uniformly charged ring = $$ \frac { Q z } { 4π \epsilon (R²+ z²)^{3/2} }

$$ where z is distance of the point from the center of the ring on the axis and R us the radius of the ring.

So I tried it out by taking a patch of area da at an angle theta from the x axis and rotating it around the axis, this gives you a cone whose, locus is that of a uniformly charged ring since all of the area is at the same angle theta and the surface charge density varies with theta.

My solution :

I used integration by substitution therefore u=cos ##\theta##

Now this answer matches with the required answer

But the suggested solution was :

Now im very lost in this suggested solution and I have some questions ....

From what I gathered they have taken two spheres of opposite charges and super imposed them on each other

1) How do they know that the charge is distributed like this? That half of it is negative and the other half is positive. ..

Couldn't it be some other distribution?

2) I have derived this formula for electric field in a cavity when the cavity was in a wholely positive sphere...doesnt the half negative and half positive distribution change the formula a bit?

My solution :

I used integration by substitution therefore u=cos ##\theta##

Now this answer matches with the required answer

But the suggested solution was :

Now im very lost in this suggested solution and I have some questions ....

From what I gathered they have taken two spheres of opposite charges and super imposed them on each other

1) How do they know that the charge is distributed like this? That half of it is negative and the other half is positive. ..

Couldn't it be some other distribution?

2) I have derived this formula for electric field in a cavity when the cavity was in a wholely positive sphere...doesnt the half negative and half positive distribution change the formula a bit?