Calculating Charge on a Sphere Given Radius & Potential

[BMcN]

I feel like the answer is staring me in the face, and no doubt it is

But how do I find the charge on a conducting sphere, given its radius and potential?

 

[Meir Achuz]

V=Q/R is staring you in the face.

 

[kyle8921]

I can assure you that finding the charge on a conducting sphere is not as daunting as it may seem. In fact, it can be easily calculated using a simple formula. The key factor in this calculation is the capacitance of the sphere, which depends on its radius and the material it is made of.

To find the charge on a conducting sphere, we can use the formula Q = CV, where Q is the charge, C is the capacitance, and V is the potential. The capacitance of a conducting sphere can be calculated as C = 4πε₀r, where ε₀ is the permittivity of free space and r is the radius of the sphere.

So, if we know the radius of the sphere and the potential, we can easily calculate the charge using the above formula. For example, if the sphere has a radius of 10 cm and a potential of 20 volts, the charge on the sphere would be Q = (4πε₀)(10 cm)(20 V) = 2513.27 Coulombs.

It is also important to note that the charge on a conducting sphere is distributed evenly on its surface. This means that the charge density (charge per unit area) can be calculated as σ = Q/A, where A is the surface area of the sphere.

I hope this explanation helps you in your calculations. Remember, as a scientist, it is important to always approach problems with a logical and systematic approach. Good luck with your calculations!