What Happens to Charge When Capacitor Plate Separation Doubles?

In summary, when the separation between the plates of a parallel plate capacitor is doubled while the potential difference is held constant, the magnitude of the charge on the plates will be cut in half. This is because the charge is inversely proportional to the separation, according to the equation Q = εoA/2d. The answer key is incorrect, as the charge should not be doubled in this scenario. However, the slight error in the formula does not affect the conclusion.
  • #1
physgrl
138
0

Homework Statement



If the separation between the plates of a parallel plate capacitor is doubled and the potential difference is held constant by a battery, the magnitude of the charge on the plates will:

*a. double

b. quadruple

c. be cut in half

d. not change

Homework Equations



CV=Q
C=εoA/2d

The Attempt at a Solution



CV=Q
C proportional to Q
εoA/2d proportional to Q
1/d proportional to Q

now if the separation d is doubled the charge Q should be cut in half instead of doubled (as the answer key says) right? so have I made a mistake? Is it supposed to be done differently?
 
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  • #2
Hi physgrl! :smile:

You are right and the answer key is wrong.

Btw, I have a different formula for the capacitance of 2 parallel plates.
It's ##C={\epsilon A \over d}##, as you can see on the wiki page: http://en.wikipedia.org/wiki/Capacitance

But that does not change your line of reasoning, which is correct.
 
  • #3
ohh yeah the 1/2 was a mistake...thanks
 

FAQ: What Happens to Charge When Capacitor Plate Separation Doubles?

What is capacitance?

Capacitance is the ability of a material or device to store an electrical charge.

2. How is capacitance measured?

Capacitance is measured in units of Farads (F) and is typically measured using a capacitance meter or by using the formula C = Q/V, where C is capacitance, Q is charge, and V is voltage.

3. What factors affect capacitance?

The capacitance of a material or device is affected by the distance between the two conducting plates, the size of the plates, and the type of material between the plates.

4. How is capacitance related to charge?

Capacitance is directly proportional to charge, meaning that as the amount of charge increases, so does the capacitance.

5. What are some real-life applications of capacitance and charge?

Capacitors, which rely on capacitance and charge, are used in a variety of electronic devices such as computers, televisions, and cell phones. Capacitors are also used in power grids to help regulate voltage and store energy. Additionally, capacitance is important in the functioning of the human body, specifically in the nervous system and the way our cells maintain a balance of charge.

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