Absolute potential from sphere.

In summary, to find the absolute potential at a distance of 3m from the center of a conducting sphere with a surface charge density of 1 pC/m^2 and a medium of relative permittivity 2, we can use the equation V=Q/4∏εr where r is the distance from the center of the sphere. By plugging in the appropriate values, we get an absolute potential of 47.0809uV, which matches the answer given in the 5th edition of Electromagnetics with Applications.
  • #1
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Homework Statement



A conducting sphere of 5-cm radius has a surface charge density of 1 pC/m^2. If the medium of relative permittivity is 2. How can we find the absolute potential at a distance of 3m from the center of the sphere?

Homework Equations



V=Q/4∏εr

The Attempt at a Solution


In this case, i make r=3, and then sub to formula. Is that right??
 
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  • #2
The charge caused by the sphere, if you integrated over the surface of the sphere, would be 4*pi*r^2*1pC/m^2, where r=0.03m. Which equals pi/100 pC. Really, just the surface area of the sphere times the charge density.
Plugging this charge into the equation as "Q", with ε=2*8.85*10^-12, r=3m, we get:
(0.0314159)*10^-12/(3*4*pi*8.85*2*10^-12)= 47.0809*10^-6V or 47.0809uV. Which is the answer given in your book, assuming you're using the 5th edition of Electromagnetics with Applications.
 

FAQ: Absolute potential from sphere.

What is absolute potential from sphere?

The absolute potential from sphere is the potential energy of a point in space surrounding a spherical object. It is a measure of the work required to bring a unit positive charge from infinity to a specific point in space outside the sphere, without disturbing the charge distribution on the surface of the sphere.

How is absolute potential from sphere calculated?

The absolute potential from sphere is calculated using the equation V = kQ/r, where V is the potential energy, k is the Coulomb constant, Q is the charge of the sphere, and r is the distance from the center of the sphere to the point in space.

What is the relationship between absolute potential and electric field?

The absolute potential and electric field are related by the equation E = -∇V, where E is the electric field, V is the absolute potential, and ∇ is the gradient operator. This relationship shows that the electric field is the negative gradient of the absolute potential.

Does the absolute potential from sphere depend on the charge distribution on the surface of the sphere?

No, the absolute potential from sphere does not depend on the charge distribution on the surface of the sphere. It only depends on the total charge of the sphere and the distance from the center of the sphere to the point in space.

What is the difference between absolute potential and relative potential?

The absolute potential is a measure of the potential energy at a specific point in space, while the relative potential is the difference in potential between two points in space. The absolute potential is always positive, while the relative potential can be positive, negative, or zero.

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