Induced charge on a plane

In summary, the group is discussing the charge induced on an uncharged conductor. One person uses the rule of induced charge to determine that the charge density on the bottom of the conductor must be -η and on the top must be η. However, another person uses Gauss law and obtains a charge density of -η/2 on the bottom, and the tutor and professor agree. The first person's method is only applicable to grounded conductors, while the conductor in question is isolated.
  • #1
athrun200
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attachment.php?attachmentid=44393&stc=1&d=1330230514.jpg

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 can't apply the rule of induced cahrge here?
 

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  • #2
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.
 
Last edited:
  • #3
But it seems my question is a plane.
 
  • #4
athrun200 said:
But it seems my question is a plane.

Sorry, my mistake. I edited the previous reply.
 
  • #5
Thx a lot
I understand now
 

What is induced charge on a plane?

Induced charge on a plane refers to the redistribution of electric charge on a conductive surface when it is placed in an external electric field. This results in a temporary separation of charges, with one side of the plane becoming positively charged and the other side becoming negatively charged.

How does induced charge on a plane occur?

Induced charge on a plane occurs due to the principle of electromagnetic induction. When a conductive plane is placed in an external electric field, the free electrons in the plane are either attracted or repelled, causing a separation of charges.

What factors affect the amount of induced charge on a plane?

The amount of induced charge on a plane is affected by the strength of the external electric field, the distance between the plane and the source of the field, and the size and shape of the conductive surface.

What is the significance of induced charge on a plane?

Induced charge on a plane plays a crucial role in various practical applications, such as in the functioning of capacitors, sensors, and electronic devices. It also helps in understanding the behavior of electric fields and their effects on conductive surfaces.

How can induced charge on a plane be controlled or manipulated?

Induced charge on a plane can be controlled or manipulated by adjusting the strength and direction of the external electric field, changing the distance between the plane and the source of the field, and altering the shape and size of the conductive surface.

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