Question

The physical quantity obtained by the line integral of electric field is:
A) $N{C}^{-1}$
B) $V{m}^{-1}$
C) $J{C}^{-1}$
D) $C^2{N}^{-1}m-1$

Answer 1

Hint: On integrating electric fields linearly we obtain potential as a result. The potential is defined as the energy required by a unit charge to travel from infinite to a point inside an electric field. So when we integrate electric field we obtain potential.

Complete step by step answer:
The physical quantity obtained by the line integral of the electric field is potential and its unit is $J{C}^{-1}$. Potential is the energy per unit charge. The electric field is the region in which a charge applies force of attraction or repulsion on another charge. The basic meaning of the line integral of electric field is that it is the addition of all values of electric field at different points. Or the sum of the product of electric fields and the distance of the position where the field is calculated.

The product of electric field and distance gives potential as a result. Different charges of different magnitude have different electric fields and potential. When the magnitude of electric field is given in the form of a mathematical function then to calculate potential we have to find the line integral of that function.

Note: Since the unit of electric field is $N{C}^{-1}$ this does not mean that the line integral will give the same physical quantity. In line integration the electric field is multiplied with the distance to give the potential. And the unit of potential is $J{C}^{-1}$.