Why do the electrostatic field lines not form closed loops?

Hint:The electrostatic field lines are the lines that are used to represent the electric field generated by the static charge. Here, we will use Maxwell’s equation to describe the nature of closed loops in an electrostatic field.

Complete answer:
Electrostatic field lines are the field lines that start from a positive charge and end at negative charge. It does not come back to the positive charge after arriving at the negative charge. The figure below shows the electrostatic file lines between the positive and the negative charge.

Consider a positive charge. As we know, a positive charge induced electric field away from it, therefore, its electrical field lines will be in an outward direction. Now, from the Maxwell equation, we get Div. of B is zero because the magnetic field does not exist in monopoles. Also, Div. of E is not zero because the electric field exists in monopoles.

But due to the closed field, the Div. of the field will be zero. This means that the field lines must terminate on the same charge from which it originated, which is not possible.Therefore, the electrostatic field lines originate from the positive charge and terminate at the negative charge. That is why electrostatic field lines do not form closed loops.

Note:Electric field lines will occur when there will be a potential difference. But, when there will be a closed-loop there will be no potential difference between the charges. Therefore, there will be no electric field between the charges, which is not possible.