An induced electric field is a non conservative field Which

An induced electric field is a non conservative field. Which of the following statement is correct? the work made by the field on an electric charge depends only on the initial and final position. the work made by the field on an electric charge to bring the charge through a closed path to the same position is zero. the work made by the electric field on an electric charge depends on the path. the work made by the electric field on an electric charge is the same for paths of equal length but with different initial and final conditions

Solution

In vector calculus a conservative vector field is a vector field that is the gradient of some function, known in this context as a scalar potential.Conservative vector fields have the property that the line integral is path independent, i.e. the choice of integration path between any point and another does not change the result. Path independence of a line integral is equivalent to the vector field being 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.

All conservative vector fields like for example a conservative electric field follow these properties. In this question, properties of a non-conservative electric field is asked.

For a non-conservative field, the potential is not defined and the work done by such a non-conservative electric field not only depends on the initial and final conditions but also depends on the path.

So, the answer is (c).