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

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 [itex]-\eta[/itex].

Since it is uncharged, the charge density on the top must be [itex]\eta[/itex].

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

My tutor also said that the answer provided by professor is [itex]\frac{-\eta}{2}[/itex].

So why I cant apply the rule of induced cahrge here?

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# Induced charge on a plane

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