Energy stored in a device (Charged Capacitor)

In summary, the problem asks for the amount of energy stored in a large van de Graaf generator with a metallic sphere on top, given its radius of 2.0 m and a charge of 3x10-5 C. The equation used to solve this is U = 1/2C(ΔV)^2, where Q is given and ΔV is found using the formula V = Q/(4∏ε0r). By substituting for V, the final equation is U = Q2/2C. The radius of the generator is not necessary to solve the problem.
  • #1
Parad0x88
74
0

Homework Statement


The metallic sphere on top of a large van de Graaf generator has a radius of 2.0 m. Suppose that the sphere carries a charge of 3x10-5 C. How much energy is stored in this device?

Homework Equations


So the equation I must use is this: U = 1/2C(ΔV)^2
Q is given; 3 x 10 ^ -5C
To find ΔV, I'd first the formula :V = Q/(4∏ε0r)



The Attempt at a Solution


Then it's simply a matter of plugging the numbers. The formula I'm not sure is how to find ΔV from the information, I'm not sure I'd be using the right one.
 
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  • #2
What's the magic word beginning with d ?
 
  • #3
CWatters said:
What's the magic word beginning with d ?

Oh, I have to find the charge density don't I? Bear with me, I'm still quite confused with all of that...

So, charge density of a sphere: p = Q/V, V = (4∏r3)/3

Would I use this as my Q in the above formula?
 
  • #4
I meant d for differentiate .

Somewhat informally..

Q=VC
V=Q/C
dV = dQ/C

dQ = the amount of charge when fully charged - the amount of charge when discharged

= 3x10-5 - 0
 
  • #5
CWatters said:
I meant d for differentiate .

Somewhat informally..

Q=VC
V=Q/C
dV = dQ/C

dQ = the amount of charge when fully charged - the amount of charge when discharged

= 3x10-5 - 0

Ok I'm sorry but I'm not following you on this one, this isn't something I've seen in class
 
  • #6
It's probably simpler than you think.

The max energy case is with it charged to some voltage V, The minimium energy state is with it discharged (zero volts) so ΔV is just V. Likewise for ΔQ.

U = 1/2C(V)2

now
Q=VC so
V = Q/C

then substitute for V giving

U = 1/2*C*(Q/C)2
= Q2/2C
 
  • #7
CWatters said:
It's probably simpler than you think.

The max energy case is with it charged to some voltage V, The minimium energy state is with it discharged (zero volts) so ΔV is just V. Likewise for ΔQ.

U = 1/2C(V)2

now
Q=VC so
V = Q/C

then substitute for V giving

U = 1/2*C*(Q/C)2
= Q2/2C

Thanks! It is simpler than I thought... So in that case I don't need the radius of the generator to solve it, it's basically an unnecessary information given?
 

What is energy stored in a charged capacitor?

Energy stored in a charged capacitor refers to the potential energy that is stored in the electric field between the two plates of the capacitor. This energy is stored when an electric charge is applied to the capacitor, causing one plate to become positively charged and the other to become negatively charged.

How is the energy stored in a charged capacitor calculated?

The energy stored in a charged capacitor can be calculated using the formula E= 1/2 CV^2, where C is the capacitance of the capacitor and V is the voltage across it. This formula is derived from the relationship between charge, voltage, and capacitance.

What factors affect the amount of energy stored in a charged capacitor?

The amount of energy stored in a charged capacitor is affected by the capacitance and the voltage. A higher capacitance or voltage will result in a greater amount of energy being stored in the capacitor. Additionally, the type of dielectric material used in the capacitor can also affect the amount of energy stored.

How is the energy released from a charged capacitor?

The energy stored in a charged capacitor can be released by connecting the two plates with a conductor, allowing the electric charge to flow from one plate to the other. This process is known as discharging and the energy is released in the form of electrical current.

What are some practical applications of energy stored in a charged capacitor?

The energy stored in a charged capacitor is used in a variety of electronic devices such as flash cameras, strobe lights, and defibrillators. It is also used in power systems to regulate voltage and in circuitry to filter out unwanted signals. Capacitors are also used in energy storage systems, such as electric vehicles and renewable energy technologies.

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