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