What Is the Correct Induced Charge on an Uncharged Conductor?

[athrun200]

The question itself is easy. E field at 2 is zero. E field at other points are of magnitude $\frac{\eta}{2\epsilon}$

But I am arguing with my classmate and tutor that what is the charge induced on the uncharged conductor.

For me, I simply use the rule induced charge (charge of same magnitude but different sign will be induced) to conclude that the charge density on the bottom of the conductor must be $-\eta$.
Since it is uncharged, the charge density on the top must be $\eta$.

But my classmate use Gauss law and obtain that the charge density on the bottom of the conductor is $\frac{-\eta}{2}$.

My tutor also said that the answer provided by professor is $\frac{-\eta}{2}$.

So why I can't apply the rule of induced cahrge here?

 

[Hassan2]

If the charge density on the top of the uncharged conductor was η, the field in region 1 would be η/ε which is not correct.
The rule of induced charge is applicable to grounded conductors. Here the uncharged conductor is isolated.

 

[athrun200]

But it seems my question is a plane.

 

[Hassan2]

But it seems my question is a plane.

Sorry, my mistake. I edited the previous reply.

 

[athrun200]

Thx a lot
I understand now