Capacitance of concentric metal spheres

[Jimmy25]

Homework Statement

A solid metal sphere has a radius of 10.0 cm and a concentric metal sphere has a radius 10.5 cm. The solid sphere has a charge 5.00 nC. (a) Estimate the energy stored in the electric field in the region between the sphere. Hint: you can treat the pheres essentially as parallel flat slabs separated by 0.5 cm. (b) Estimate the capacitance of the two-sphere system. (c) Estimate the total energy stored in the electric field from 1/2Q^2C.

Homework Equations

The Attempt at a Solution

I stared with V=(KQ)/r but I'm pretty sure I am not right. My rationelle was to that I could treat the solid sphere as a point charge by Gauss's Law and find the potential difference between it's surface and the inside of the hollow shell. Doesn't seem right and I don't what to do about the "hint"...

 

[anathema]

Hello there,

I would like to offer some guidance on how to approach this problem.

Firstly, you are correct in using Gauss's Law to treat the solid sphere as a point charge. This will allow you to find the electric field at any point in the region between the spheres. Remember, the electric field is a vector quantity, so you will need to consider both the magnitude and direction of the electric field.

Next, the hint suggests treating the spheres as parallel flat slabs separated by 0.5 cm. This means that you can use the formula for the electric field between two parallel plates, E=V/d, where V is the potential difference and d is the distance between the plates. You can use this formula to find the electric field between the two spheres.

To estimate the energy stored in the electric field, you can use the formula U=1/2ε0E^2, where ε0 is the permittivity of free space. This will give you the energy per unit volume in the region between the spheres. To find the total energy, you will need to multiply this value by the volume of the region between the spheres.

For part (b), you can use the formula C=Q/V, where Q is the charge on one of the spheres and V is the potential difference between the two spheres. Remember to consider the direction of the electric field when calculating the potential difference.

Finally, for part (c), you can use the formula U=1/2Q^2C to find the total energy stored in the electric field. Remember to use the value of C that you calculated in part (b).

I hope this helps guide you in the right direction. Remember to always think carefully about the problem and use the appropriate equations. Good luck with your calculations!

 

[kerimek]

I would approach this problem by first understanding the concept of capacitance. Capacitance is a measure of the ability of a system to store electric charge. In this case, we have two concentric metal spheres with a charge on the inner sphere. The region between the two spheres can be treated as a capacitor, where the two spheres act as the two plates.

To estimate the energy stored in the electric field, we can use the formula for the energy stored in a capacitor, which is given by U = (1/2)CV^2. In this case, the voltage (V) between the two spheres can be calculated by dividing the charge on the inner sphere (Q) by the distance between the spheres (r). Using the hint provided, we can treat the spheres as parallel flat slabs separated by 0.5 cm. This would give us a distance of 0.5 cm between the two spheres.

So, for part (a), we can estimate the energy stored in the electric field by using the formula U = (1/2)CV^2, where C is the capacitance of the system and V is the voltage between the two spheres. We can calculate the voltage by dividing the charge on the inner sphere (5.00 nC) by the distance between the spheres (0.5 cm). This gives us a voltage of 10 V. Now, to estimate the capacitance, we can use the formula C = Q/V, where Q is the charge on the inner sphere and V is the voltage between the two spheres. This gives us a capacitance of 0.5 nF.

For part (b), we can estimate the capacitance of the two-sphere system using the formula C = Q/V, where Q is the charge on the inner sphere and V is the voltage between the two spheres. We already know the charge on the inner sphere (5.00 nC) and we can calculate the voltage by dividing it by the distance between the spheres (0.5 cm). This gives us a capacitance of 0.5 nF.

For part (c), we can estimate the total energy stored in the electric field by using the formula U = (1/2)Q^2C. We already know the charge on the inner sphere (5.00 nC) and the capacitance of the system (0.5 nF). Plugging these values into the formula