Question

What do you mean by line integral of electric field?

Answer 1

Are you familiar with ordinary integrals? When we write an integral, we specify the “direction” that the integral is taken in. So, for example, when we write:[math]\displaystyle\int f(x)dx[/math]We mean to take the integral along the[math]x[/math]direction (that’s what the[math]dx[/math]specifies).A line integral is a similar idea, but rather than take the integral along one of the axis directions, we take the integral along some other path, which may even be curved. In the caseof your example, we integrate the electric fieldalong the electric field vectoritself. Since, in general, the electric field points in different directions in different parts of space, this means that the direction we integrate in can also change as we proceed along the path of integration.The reason for doing this is that the line integral of the electricfield between two points is precisely equal to the potential difference between those two points. This makes sense, since the electric fieldis the gradient (three-dimensional spatial derivative) of the potential. So, integrating the electric field is the complementary operation to differentiating the potential.

Answer 2

Answer:

Refer to attachment please.