In the previous problem, suppose the battery remains connected while the plates are pulled apart

step 1 So this question is actually a continuation of question 81. So in question 81, what we have is w

In the previous problem, suppose the battery remains...

Key Concepts

Capacitance and Geometry

Capacitance is a measure of a capacitor’s ability to store electric charge and is determined by the geometry of its components. In a parallel-plate capacitor, capacitance is directly proportional to the plate area and inversely proportional to the separation between the plates. When the plates are pulled apart while the battery remains connected, the capacitance decreases because of the increased separation, modifying the relationship between charge and voltage.

Constant Voltage Condition

When a battery is connected to a capacitor, it maintains a fixed voltage across the capacitor's plates regardless of changes in capacitance. This constant voltage condition means that as the geometry of the capacitor changes, the system must adjust the amount of charge on the plates so that the voltage remains unchanged. This contrasts with an isolated capacitor, where the charge would remain constant instead.

Charge Adjustment in Capacitors

Under a constant voltage condition, any decrease in capacitance due to an increase in plate separation necessitates a decrease in the stored charge (since Q = CV) to maintain the same potential difference. This concept of charge redistribution is crucial for understanding how connected capacitors respond to changes in their physical configuration.

Stored Energy in a Capacitor

The energy stored in a capacitor is given by the formula U = 1/2 CV². With the voltage kept fixed by the battery, a reduction in capacitance results in a corresponding decrease in stored energy. Analyzing the change in stored energy helps in understanding the work interactions within the system as the plates are moved apart.

Work and Force Considerations

The process of pulling the plates apart involves mechanical work, which is closely related to the energy changes in the capacitor. When the capacitor is connected to a battery, the battery can do work to maintain the voltage as the capacitor's energy changes. Furthermore, there is an attractive force between the oppositely charged plates, and understanding how this force is overcome during separation provides insights into the interplay between electrical forces and mechanical work.

Transcript

00:01 So this question is actually a continuation of question 81.

00:06 So in question 81, what we have is we have a parallel plate capacitor, and each plate is a square of side 0 .2 meter.

00:19 And these two plates also have a separation of 0 .80 centimeter.

00:26 So in the previous question, what happens is that we have these two plates that are connected to a source of 120 volts.

00:42 And then we find out various properties of this plate, in particular in question 81, we find that the capacitor, the capacitance of this is 4 .4 3 times 10 to the negative 11.

00:59 We find that the charge in it is cv, which is 5 .3, 2 times 10 to the negative 9 column.

01:10 We find the electric field in it, which is v.

01:14 D, which is 1 .5 times 10 to the 4ths per meter.

01:20 And we also find the energy.

01:23 U is the energy.

01:29 U equals one half of qv or the other expressions of it which is 3 .19 .19 times 10 to the negative 7 so these are the four quantities you find in the previous problem if you did if you did not get the same numbers maybe you should go back and watch the video for question 81 and then in 81 what happens is that the battery is then removed and the separation is changed to twice its previous separation.

02:01 So that was all in question 81.

02:05 What this question, question 82 asks is what if we separate them but without removing the battery? so what this means is that when we separate them to twice this distance, c is epsilon a over 2d.

02:28 So i will call this not.

02:30 Everything not.

02:32 So it becomes one half of the previous value because it separates them as distance increases and the capacitance is half of its original value...

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