Introduction:
Force field lines are used to represent the direction and strength of a force in a given field. In the case of an electric field, the force field lines indicate the direction in which a positive charge would move if placed in the field. To find the equation of force field lines, we need to start with the expression for the electric field.

Step 1: Understand the Electric Field Expression:
The electric field (E) at a point in space is defined as the force per unit positive charge experienced by a test charge placed at that point. The electric field is a vector quantity and is given by the expression:
E = k * Q / r^2
where E is the electric field, k is the electrostatic constant, Q is the charge creating the field, and r is the distance from the charge to the point in space.

Step 2: Analyze the Electric Field Expression:
To find the equation of force field lines, we need to analyze the electric field expression. The electric field is directly proportional to the charge creating the field (Q) and inversely proportional to the square of the distance (r) from the charge. This means that the electric field is stronger closer to the charge and weaker farther away from the charge.

Step 3: Determine the Direction of the Electric Field:
The direction of the electric field is given by the direction in which a positive charge would move if placed in the field. Electric field lines always point away from positive charges and towards negative charges. To determine the direction of the electric field lines, we can use the principle that opposite charges attract each other and like charges repel each other.

Step 4: Plotting the Force Field Lines:
To plot the force field lines, we can use the electric field expression to determine the direction and strength of the electric field at different points in space. We can choose a set of points in space and calculate the electric field at each point using the given expression. Based on the direction and strength of the electric field, we can then draw arrows to represent the force field lines.

Step 5: Equation of Force Field Lines:
The equation of force field lines can be determined by finding a mathematical function that describes the path followed by the force field lines. This function will depend on the specific distribution of charges creating the electric field. In some cases, the equation of force field lines may be a simple equation, such as a straight line or a circle. In more complex cases, the equation of force field lines may involve higher-order functions or require numerical methods to determine.

Conclusion:
To find the equation of force field lines, we need to start with the expression for the electric field and analyze its properties. By understanding the direction and strength of the electric field, we can plot the force field lines and determine their equation. The equation of force field lines will depend on the specific distribution of charges creating the electric field and may involve simple or complex mathematical functions.