Question

The diagram represents the electric lines of force emerging from a charged body. If the electric field at A and B are ${{E}_{A}}$ ​ and ${{E}_{B}}$ ​ respectively and when the displacement between A and B is $r$, then what is the correct answer given below?

$\begin{align}
  & A.{{E}_{A}}>{{E}_{B}} \\
 & B.{{E}_{A}}<{{E}_{B}} \\
 & C.{{E}_{A}}=\dfrac{{{E}_{B}}}{r} \\
 & D.{{E}_{A}}=\dfrac{{{E}_{B}}}{{{r}^{2}}} \\
\end{align}$

Answer 1

Hint: The field lines will be representing the magnitude and also the direction of the electric field. In a specific way, we can say that the field will be strong at points where the field lines are closely spaced. In the same sense, the field will be weak at points where they are far apart. This will help you in answering this question.

Complete step by step solution:
Electric field lines are defined as the better idea of visualizing electric fields. Electrical lines of force are explained as a way or path, it can be sometimes straight or curved so that the tangent there will give the direction of the intensity of the electric field at that position at any location. Therefore, the field lines will be representing the magnitude and also the direction of the electric field. In a specific way, we can say that the field will be strong at points where the field lines are closely spaced. In the same sense, the field will be weak at points where they are far apart. Therefore greater the number of electric lines of force per unit area in a certain region, the more will be the strength of the field.
Hence we can write that,
${{E}_{A}}>{{E}_{B}}$
The correct answer is given as option A.

Note: There are so many properties for electric field lines. The field lines will not intersect with each other. The field lines will be orthogonal to the surface of the charge. The magnitude of the charge and the number of field lines will be proportional to each other.