How to Calculate Field Lines

The electric field lines coming out of a point charge are symmetrical, similar to spokes on a wheel.

In order to calculate electric field lines, you need to know the magnitude of the field and its direction at a point. The electric field is a vector quantity, which means it has a direction associated with its magnitude at each point in space. A vector has three possible directions, and in the Cartesian coordinate system, these are indicated by the unit vectors i,j,k in the x,y and z directions respectively. The x, y and z axes are directed along the horizontal, vertical and out of the page, respectively.

Instructions

1. Write down the equation for the electric field at a point. For example, the electric field due to a point charge is given by Coulomb's law--E=q/(4*pi*epsilon0*R^2) r--where r is a radial coordinate unit vector pointing out radially from the center; pi is a constant derived from the ratio of the circumference of a circle and the diameter and has a value of 3.14159; epsilon0 is the permittivity of free space with a value of 8.85e-12; q is the charge of the particle; and R is the distance from the particle to the place where the field is being calculated.

2. Get the distance from the point charge to where the electric field is being calculated and convert the units of this value to meters, if necessary. The variable R in the equation for the electric field is squared with the units length^2. If you want to convert it, first get the relation between its units and meters, square this value and then since R is in the denominator of the formula, you will need to multiply the equation by it. For example, if you are given a distance in centimeters, then use the relation 1 cm = 0.01 m. Next, square these numbers to get (1 cm)^2 = (0.01 m)^2, which can be rewritten as 1 cm^2 = 0.01^2 m^2, and then multiply the equation for the electric field by 0.01^2, which equals 1e-4, as follows: E= 1e-4* (q/(4*pi*epsilon0*R^2) ) r N/C.

3. Get the direction of the electric field vector. The electric field is directed outward from a positive charge and towards the negative. For the case of a point charge, the field is symmetrical about the charge, and therefore the field lines come out or go in to the charge in a similar way to the spokes on a bicycle wheel. However, if a charge of opposite sign is placed in the vicinity of the point charge, then the electric field around it is no longer symmetrical, and now the components in the x,y and z directions of the electric field at a point need to be calculated using vector analysis. The relative magnitudes of each component of the electric field indicates the direction of the vector. For example, if the electric field is given by E=100 i + 0 j + 0 k N/C , then it is directed along the x axis, whereas E=100 i + 100 j + 0 k N/C has equal weighting in the x and y directions and will therefore be a vector originating from the origin at 45 degrees to both axes. There are alternative coordinate systems such as cylindrical and spherical coordinates that might be easier to use, depending upon what you are modeling.

References

• “University Physics”; Hugh D. Young; 1992