What is the Total Induced Charge on a Grounded Conducting Plane?

This force is present for all q, so to ensure the plane is in equilibrium, the sum of all these forces should be zero. This means that the induced charge q' should be such that q*q'/(2L)^2 is a constant (i.e. K). The only solution for this is q'= -q. In summary, the answer is D because the induced charge on the plane is equal and opposite to the charge q, as determined by Coulomb's law. This can also be derived mathematically or understood intuitively by considering the forces acting on the charge q and the resulting equilibrium state of the plane.
  • #1
dudu1
3
0
A positive charge Q is located at a distance L
above an infinite grounded conducting plane.
What is the total charge induced on the plane?
(A) 2Q
(B) Q
(C) 0
(D) -Q
(E) -2Q

I know the answer is C, but why? Thanks a lot!
 
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  • #2
The answer is D. The induced charge is equal and opposite to the charge q.

I refer you to pg. 123 of Griffith's "Introduction to Electrodynamics" for a derivation.

But by intuition alone, it wouldn't make sense for the induced surface charge to be zero; the presence of the charge q will tend to push positive charge (or the opposite, attract negative charge) to the surface closest to it. This causes an "image charge" to be produced within the conducting plane. The force experienced by the charge q is equal to that of a charge -q located a distance L beyond the surface of the plane; i.e. the force will be -q*q/(2L)^2 (I have dropped the constants that show up in Coulomb's law).
 

FAQ: What is the Total Induced Charge on a Grounded Conducting Plane?

1. What is induced charge?

Induced charge refers to the separation of positive and negative charges in a conductor that is brought near an external electric field. This separation is caused by the redistribution of electrons within the conductor.

2. How is induced charge different from static charge?

Induced charge is different from static charge in that it is temporary and only occurs when a conductor is placed in an external electric field. Static charge, on the other hand, is a permanent imbalance of electric charges on an object.

3. What is the mechanism behind induced charge?

The mechanism behind induced charge is the movement of free electrons within a conductor in response to an external electric field. When a conductor is placed in an electric field, the electrons within it shift to one end, creating a temporary separation of charges.

4. Can induced charge be controlled?

Yes, induced charge can be controlled by changing the strength or direction of the external electric field. This can be done by altering the distance between the conductor and the source of the electric field, or by changing the magnitude and direction of the electric field itself.

5. What are some practical applications of induced charge?

Induced charge has various practical applications, including electrostatic painting, electrostatic precipitators for air pollution control, and capacitive touch screens on electronic devices. It is also used in scientific research to study the behavior of electric fields and charges.

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