# Heat liberated after connecting two plates

#### Saitama

The electric field is basically nonzero everywhere except inside of the conductors. The LARGE electric field is between the two plates. I think this is the approximation they are expecting you to make. You are getting distracted by details. Just consider the approximate E field between the plates.
Thanks Dick, can you help me with finding the final charges? :)

#### ehild

Homework Helper
Pranav, when the plates get connected, they become a single conductor, one side having more charge than the other. What happens if you touch a metal plate with a charged rod? The charges go over to the plate and disperse on it till the charge density is the same everywhere. The same happens here, the two plates are equivalent, the 4q charge will disperse evenly on the plates.

Now look at the picture. The two plates with their 4q charge look a single tiny charged object from far away. (At great distance, the field is like that of a point charge), and the field outside the plates does not depend on the field inside. The energy of the whole set-up is the sum of the field outside and the field inside. When the plates are connected there is no field inside. So what is the energy difference between the field before and after connecting the plates?

ehild

#### Attachments

• 10.6 KB Views: 220

#### Saitama

Pranav, when the plates get connected, they become a single conductor, one side having more charge than the other. What happens if you touch a metal plate with a charged rod? The charges go over to the plate and disperse on it till the charge density is the same everywhere. The same happens here, the two plates are equivalent, the 4q charge will disperse evenly on the plates.

Now look at the picture. The two plates with their 4q charge look a single tiny charged object from far away. (At great distance, the field is like that of a point charge), and the field outside the plates does not depend on the field inside. The energy of the whole set-up is the sum of the field outside and the field inside. When the plates are connected there is no field inside. So what is the energy difference between the field before and after connecting the plates?

ehild
Nice explanation ehild. Thanks!

The energy difference is equal to the energy stored between the plates before the switch is closed.

#### ehild

Homework Helper
Nice.

Before searching for equations which can be connected with a problem, try to imagine that you are involved in the situation. For example, in this problem, imagine two dance rooms of the same size, and there are 300 people in one of them and only 100 people in the other one. The door between the rooms is locked at the beginning. You are in the more crowded room. Somebody opens the door. What do you do? And how many people will be present in both rooms at the end?
Here the electrons are the people, the rooms are the plates, and you are an electron on the more crowded plate...

ehild

#### Dick

Homework Helper
The same happens here, the two plates are equivalent, the 4q charge will disperse evenly on the plates.
Maybe more accurate to say that the 4q charge is evenly spread over the outside surfaces of the plates? There won't be any to speak of on the inside surfaces.

#### ehild

Homework Helper
Maybe more accurate to say that the 4q charge is evenly spread over the outside surfaces of the plates? There won't be any to speak of on the inside surfaces.
Of course, you are right, evenly spread on the outside of the plates.

ehild

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving