Spherical Capacitor: Calculating Capacitance in pF

In summary, the problem involves a spherical capacitor with a larger conducting shell charge -Q and a smaller conducting sphere with charge Q. The outer shell has inner and outer radii of 11.0 cm and 13.0 cm, respectively. The question asks for the capacitance of the system, which can be calculated using the equation C = \frac{Q}{\Delta V}. However, the presence of a thickness in the outer shell complicates the calculation. The method used when there is no thickness, -\int_{r_1}^{r_2} kQ\frac{dr}{r^2}, is not applicable here. The distribution of -Q on the outer shell is also unclear.
  • #1
professordad
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Homework Statement



A spherical capacitor consists of a spherical conducting shell charge [itex]-Q[/itex] concentric with a smaller conducting sphere of radius [itex]4.0[/itex] cm and charge [itex]Q[/itex]. The larger conducting shell has inner and outer radii of [itex]11.0[/itex] cm and [itex]13.0[/itex] cm, respectively. What is the capacitance of the system in pF?

Homework Equations



[itex]C = \frac{Q}{\Delta V}[/itex]

The Attempt at a Solution



I don't know what to do when the outer shell has a thickness. I know that when it doesn't have a thickness you would do
[itex] -\int_{r_1}^{r_2} kQ\frac{dr}{r^2} [/itex]
where [itex]r_1[/itex] and [itex]r_2[/itex] are the inner and outer radii, respectively. But here what do you do for [itex]r_2[/itex]?

Thanks.
 
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  • #2
How would -Q be distributed on the outer shell ?
 
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FAQ: Spherical Capacitor: Calculating Capacitance in pF

What is a spherical capacitor?

A spherical capacitor is a type of capacitor that consists of two concentric spherical conductors, separated by a dielectric material. It is used to store electric charge and energy.

How do you calculate the capacitance of a spherical capacitor?

The capacitance of a spherical capacitor can be calculated using the formula C = 4πε₀r, where C is the capacitance, ε₀ is the permittivity of free space, and r is the radius of the inner conductor.

What is the unit of capacitance for a spherical capacitor?

The unit of capacitance for a spherical capacitor is picofarads (pF). This unit is equivalent to 10^-12 farads and is commonly used for measuring small capacitance values.

How does the dielectric material affect the capacitance of a spherical capacitor?

The dielectric material between the two conductors of a spherical capacitor affects the capacitance by changing the electric field strength between the conductors. A higher dielectric constant will result in a higher capacitance, while a lower dielectric constant will result in a lower capacitance.

What factors can affect the accuracy of capacitance calculations for a spherical capacitor?

The accuracy of capacitance calculations for a spherical capacitor can be affected by factors such as the precision of the radius measurement, the dielectric constant of the material, and the presence of any external electric fields that may interfere with the electric field between the conductors.

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