Which of the following are conservative electric field?
The conservative nature of electrostatic fields establishes the electrostatic field as a conservative field. This opens the door for conservation of energy and the work-kinetic energy theorem in discussions of electric fields and electric forces.
Why is electric field called conservative?
The work done to carry a test charge (q) from point A to another point B in the field due to Q does not depend upon the path followed. Electric field depends upon the initial and final positions A and B. Electric fields are independent of the path followed. So we say that the electric field is conservative in nature.
When electrostatic field is conservative Which of the following is true?
Work done by the electrostatic force is independent of the path followed by it, and it depends only on the initial and final positions. For example, work done in moving a unit positive charge in a closed loop of an electric field is zero. So,electrostatic force is a conservative force.
Which field is associated with capacitor?
electric field
Is electrostatic field Solenoidal?
Note: A function that has zero divergence is called solenoidal. Functions that have zero curl are called irrotational. In electrostatics electric fields are irrotational and magnetic fields are irrotational only in regions of space where there are no current sources.
What is the difference between an irrotational field and a solenoidal field?
A Solenoidal vector field is known as an incompressible vector field of which divergence is zero. On the other hand, an Irrotational vector field implies that the value of Curl at any point of the vector field is zero.
Can a vector field be both irrotational and solenoidal?
An irrotational vector field is a vector field where curl is equal to zero everywhere. By Helmholtz’s theorem, any vector field can be written as the sum of a gradient and a curl (or, in other words, an irrotational and incompressible vector field).
How do you know if F is conservative vector field?
This condition is based on the fact that a vector field F is conservative if and only if F=∇f for some potential function. We can calculate that the curl of a gradient is zero, curl∇f=0, for any twice continuously differentiable f:R3→R. Therefore, if F is conservative, then its curl must be zero, as curlF=curl∇f=0.
Is every irrotational vector field conservative?
A conservative vector field is also irrotational; in three dimensions, this means that it has vanishing curl. An irrotational vector field is necessarily conservative provided that the domain is simply connected.
Is f’an incompressible vector field?
d) F is not irrotational and not incompressible. The terminology in this problem comes from fluid dynamics where fluids can be incompressible, irrotational. G(x, y, z) such that curl( G) = F? Such a field G is called a vector potential.
Is conservative vector field incompressible?
Under suitable smoothness conditions on the component functions (so that Clairaut’s theorem holds), conservative vector fields are irrotational, and under suitable topological conditions on the domain of F, irrotational vector fields are conservative. Moving up one degree, F is called incompressible if ∇⋅F=0.
Which vector is Solenoidal as well as Irrotational?
Just to add to the answer above, under fairly mild conditions, you can decompose a vector field (in R3) into its solenoidal and irrotational parts (Helmholtz Decomposition). So you can think of general vector fields as having “constituents”, one solenoidal and the other irrotational.
How do you know if a 3d vector field is conservative?
If a three-dimensional vector field F(p,q,r) is conservative, then py = qx, pz = rx, and qz = ry. Since F is conservative, F = ∇f for some function f and p = fx, q = fy, and r = fz.