What is the potential energy of a solid sphere?

What is the potential energy of a solid sphere?

The total energy required to assemble the sphere is the integral of dU from r=0 to r=a, or U=4πρ2a515ϵ0. Or if we wish to express the result in terms of the total charge Q of the sphere, U=35Q24πϵ0a. The energy is proportional to the square of the total charge and inversely proportional to the radius.

What is potential energy derive its formula?

W=mgh.

What is potential energy and its derivation?

Potential Energy Derivation Potential energy is the work done to take a body to a certain height. For a body with mass m, h is the distance to which it is raised and g is the gravitational force acting on the body, then work done W is given as: W = force * displacement. W = mg * h. ∴ W = mgh.

How do you find the gravitational potential at a point?

The gravitational potential of a point is equal to the potential energy that a unit mass would have at that point. It is given by V, equals, start fraction, U, divided by, m 2, end fraction,V=m2​U​ where U,U is the potential energy of a mass m 2,m2​ at that point.

What two factors determine gravitational potential energy?

Gravitational Potential Energy is determined by three factors: mass, gravity, and height.

What is the gravitational potential due to a point mass m at a distance r is?

Potential due to a point mass m at a distance r is V = – GMr .

What is gravitational potential energy find the formula for gravitational potential due to a point mass?

Key Points Near the surface of the Earth, the work done in lifting an object through a height h is the product mgh , so U=mgh . 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 .

How is electricity related to gravity?

Since electricity is the density variation of the gravity, the gravity and the electricity have the same signaling velocity c0. This can be summarized: When you have a gravity mass then you can see a object due to his electrical waves.

Why gravitational potential is a scalar?

The gravity potential is the scalar potential associated with the gravity per unit mass, i.e., the acceleration due to the field, as a function of position. The gravity potential is the gravitational potential energy per unit mass. Not every vector field has a scalar potential.

Is gravitational potential a scalar field?

If you’re just doing standard Newtonian mechanics, then the force of gravity is a vector. Force is always a vector, because it always has a direction in which it’s pointing. The gravitational potential is a scalar field, which means it just has a magnitude at any given point.

Is shear stress a vector or scalar?

Stress is neither scalar nor vector its a tensor quantity because it needs magnitude, direction and a plane for complete definition.

Why Stress is scalar?

3 Answers. Stress is a rank-two tensor that couples one 3-D vector (a direction associated with an area) to another (a force). The tensor can hold 3×3=9 values according to the various directional combinations, but for static problems, only six values can be independent.