Why divergence of electric field is zero

II To avoid the notion of distributions , it is more safe and probably more intuitive to work with the equivalent integral form of Gauss's law. The corresponding Gauss's law for magnetism. Also we should mention the well-known fact that integration theory can be appropriately generalized from non-negative functions to complex-valued functions. Yet, no matter how you feel about the Dirac delta, where there is charge, there is non-zero divergence of the electric field.

And, conversely, where there is non-zero divergence, there is charge. Now, it is not the Dirac delta that is "unrealistic" it is a perfectly well defined distribution , it is the concept of a "point charge".

Every charged thing we know has this charge distributed over a - however small - area of space, and the Dirac delta is a way to model that this area is so small that we don't care that its not point-like. And if there truly was a point-like charge, the Dirac delta would exactly describe its charge density - because the volume of a point is clearly zero, and whatever charge the thing has divided by zero is infinite.

Do not take this as a rigorous statement, this is as handwavy as it gets. There is nothing wrong with the Dirac delta as a charge or other density. It's a valid instantaneous magnetic field.

You could use Maxwell's equations to find a current density or changing electric field, but that's beyond the point. The point is:. This is really a finite magnetic field with no source or sink. It's not a matter of observing its source or sink. There's no source or sink to observe! Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams?

Learn more. Divergence of a field and its interpretation Ask Question. Asked 7 years, 4 months ago. Active 7 years, 4 months ago. Viewed 56k times. However, clearly a charge is there. So there was no escape route. Improve this question. Peter Mortensen 2, 2 2 gold badges 18 18 silver badges 24 24 bronze badges. Subhra Subhra 1 1 gold badge 3 3 silver badges 9 9 bronze badges. Start Now.

Explanation: 1. Note: 1. Thus divergence of magnetic flux density is always zero. Get Started for Free Download App. Which of the following is related with Stoke's Theorem? In which of the following cases the divergence of the electric field is zero.

Consider the following statements : Stokes' theorem is valid irrespective of 1. Shape of closed curve C 2. Type of vector A 3. Type of coordinate system 4. Whether the surface is closed or open Which of the above statements are correct? More Vector Calculus Questions Q1.

The curl of the gradient is the integral of the gradient round an infinitesimal loop which is the difference in value between the beginning of the path and the end of the path. In a scalar field there can be no difference, so the curl of the gradient is zero. We can say that the gradient operation turns a scalar field into a vector field. Note that the result of the divergence is a scalar function. We can say that the divergence operation turns a vector field into a scalar field. We can say that the curl operation turns a vector field into another vector field.

Any direction you follow will lead to a decrease in temperature. A zero slope line is a straight, perfectly flat line running along the horizontal axis of a Cartesian plane. The equation for a zero slope line is one where the X value may vary but the Y value will always be constant.

The curl is just a number at any point in that field that holds information of that field. For example, instead of a vector field one could define a scalar field of which the value is always the magnitude of the electric field.

The divergence of the electric field at a point in space is equal to the charge density divided by the permittivity of space. It is often more practical to convert this relationship into one which relates the scalar electric potential to the charge density. If you calculate all the differences of partial derivatives and they give zero, then it is a valid electric field. In the absence of time-varying magnetic field, the electric field is therefore called conservative i.

The electrostatic field or electric field due to charges is conservative but the electric field induced due to time varying magnetic field is non-conservative in nature. Induced electric field forms closed loops.

Work done by force due to induced electric field in a closed loop is not zero. These electric fields have closed field lines, so that they are non-conservative. Note: The electric field is conservative in nature. We can prove this by proving that the work done by an electric field depends only on the starting and the ending points of the cycle but not on the path taken by the electric field.

For example, if the centripetal force is gravity then it is conservative. But if the force responsible for the circular motion is static friction, like that between the tires and road of a car enabling it to turn in a circle, then both the centripetal and centrifugal forces would be non-conservative. One very common example of a conservative force that fits this definition is the force of gravity.

Some examples include the force of friction, the pull or push of a person, and air resistance drag forces, which depend on things like velocity. These forces depend on the pathway taken by the object. Conservative force, in physics, any force, such as the gravitational force between the Earth and another mass, whose work is determined only by the final displacement of the object acted upon.

Gravity is doing work on the object by pulling it towards the Earth, but since you are pushing it in the other direction, the work you do on the box and therefore the force is negative. Begin typing your search term above and press enter to search. Press ESC to cancel.