What is the self-energy of a sphere?

The work that is done in charging a thin spherical shell is stored in the form of energy. This energy stored is called self-energy.

What is gravitational self energy of a solid sphere?

The gravitational self energy U fo a uniform solid sphere is equal to the amount of work done in assembling together its infinitessimal particles initally lying infinite distance apart. IF M is the mass and R is the radius of the solid sphere, then the gravitational self energy of a solid sphere is given by.

How do you find the gravitational potential energy of a sphere?

The value of gravitational potential is given by, V = -GM/R. Case 2: If point ‘P’ lies on the surface of the spherical shell (r=R): On the surface of the earth, E = -GM/R2.

What is the gravitational self energy of a solid sphere of mass M and radius R?

Therefore, U(self-potential energy)=−21Gm2/R.

What do you mean by self-energy?

Definition of self-energy : energy that is generated in or by itself.

What is Electron self-energy?

In a condensed matter context relevant to electrons moving in a material, the self-energy represents the potential felt by the electron due to the surrounding medium’s interactions with it.

How do you find the gravitational self energy?

U=−163Gπ2(M(4/3)πR3)2(R55)=−3GM25R . This is the required gravitational self potential energy for the case of a solid sphere. So, for the case of (a) a thin uniform shell we have −GM22R and for the case of (b) a uniform sphere of mass m and radius R we have −3GM25R.

What is the gravitational potential energy of the mass m?

The gravitational potential energy, U , of a system of masses m1 and M2 at a distance r using gravitational constant G is U=−Gm1M2r U = − G m 1 M 2 r .

Is self-energy potential energy?

Self energy is energy required to bring all charge to form sphere while potential energy is because of charge on sphere.

What is self-energy in electrostatics?

In electrostatics, the energy required to assemble the charge distribution takes the form of self-energy by bringing in the constituent charges from infinity, where the electric force goes to zero.

What is self potential energy?

Hint: Gravitational self potential energy is the amount of work done to create an object of mass M formed by joining small masses of mass dm which were brought from infinity. Clearly, integration has to be performed by considering the potential created by for small mass m first.

How do you find the potential energy of a self-gravitating sphere?

For a self-gravitating sphere of constant density , mass M, and radius R, the potential energy is given by integrating the gravitational potential energy over all points in the sphere, (Kittel et al. 1973, pp. 268-269).

What is the self energy of a uniform sphere?

Now, note that m and r are related to each other through the density ρ, which is constant (sphere is uniform). We have, which is the self energy of a uniform sphere.

What is self-energy of a body?

Hence, self-energy of a body is the potential energy stored within the body as the body is assembled from free individual particles. Uniform sphere: Let us evaluate gravitational self-energy of a uniform solid sphere of mass M and radius R.

What is the self energy of a gravitational force?

Gravitational Self Energy. The gravitational potential energy of a composite system of n particles, given is called the self-energy of the system: The above energy represents the (negative of) work done in assembling the system from individual particles that were initially infinitely apart.