ELECTRICAL FIELD LINES

ELECTRICAL FIELD LINES:-

                                       Electrical field lines can be thought of a "map"that provide information about the directions and strength of electrical fields at various places. As the electrical field lines provide the information about electrical force exerted on a charge. These lines are commonly called "lines of force". For any given location the arrow point in the direction of the electrical field and their length is proportional to strength of the electrical field at that location. Such vector arrows are shown in the fig. Note that the length of arrow are longer where closer to the source charge and shorter when away from source charge.

RULES FOR DRAWING ELECTRICAL FIELD LINES:-

                  Following are the rules to draw electrical field lines:

• Object having greater charge are surrounded by more electrical field line as we know greater charge particle produce stronger electrical field. This not only give information about charge density but also about strength of electrical field at that location.
• Electrical field line are drawn perpendicular to the surface of the object where the object connects to objects surface either it is symmetrical object or irregular electrical field lines are never parallel. If the electrical field lines would be parallel then charge would accelerate and would lead to electrical current. 
•  Electrical fields never cross each other.  This is because as tangent represents the direction of electrical field if electrical field line intersects each other then at a point there would be two directions
  
  which is impossible as shown in fig 

ELECTRICAL FIELD LINES FOR TWO OR MORE CHARGES:-

Suppose that there are two positive charges - charge A (QA) and charge B (QB) - in a given region of space. Each charge creates its own electric field. At any given location surrounding the charges, the strength of the electric field can be calculated using the expression kQ/d2. Since there are two charges, the kQ/d2 calculation would have to be performed twice at each location - once with kQA/dA2 and once with kQB/dB2 (dA is the distance from that location to the center of charge A and dB is the distance from that location to the center of charge B). The results of these calculations are illustrated in the diagram below with electric field vectors (EA and EB) drawn at a variety of locations. The strength of the field is represented by the length of the arrow and the direction of the field is represented by the direction of the arrow.

Since electric field is a vector, the usual operations that apply to vectors can be applied to electric field. That is, they can be added in head-to-tail fashion to determine the resultant or net electric field vector at each location. This is shown in the diagram below.

The diagram above shows that the magnitude and direction of the electric field at each location is simply the vector sum of the electric field vectors for each individual charge. If more locations are selected and the process of drawing EA, EB and Enet is repeated, then the electric field strength and direction at a multitude of locations will be known. (This is not done since it is a highly time intensive task.) Ultimately, the electric field lines surrounding the configuration of our two charges would begin to emerge. For the limited number of points selected in this location, the beginnings of the electric field line pattern can be seen. This is depicted in the diagram below. Note that for each location, the electric field vectors point tangent to the direction of the electric field lines at any given point.

The construction of electric field lines in this manner is a tedious and cumbersome task. The use of a field plotting computer software program or a lab procedure produces similar results in less time (and with more phun). Whatever the method used to determine the electric field line patterns for a configuration of charges, the general idea is that the pattern is the resultant of the patterns for the individual charges within the configuration. Similarly we do with other charges.

PROPERTIES OF ELECTRICAL FIELD LINES:-

• Electric field lines always extend from a positively charged object to a negatively charged object, from a positively charged object to infinity, or from infinity to a negatively charged object.
• Electric field lines never cross each other.
• Electric field lines are most dense around objects with the greatest amount of charge.
• At locations where electric field lines meet the surface of an object, the lines are perpendicular to the surface.

PROBLEMS:-

NUMBER 1

Several electric field line patterns are shown in the diagrams below. Which of these patterns are incorrect? _________ Explain what is wrong with all incorrect diagrams.

SOLUTION

Answer: C, D and E

In C, the lines are directed towards a positively charged object.

In D, the lines are not symmetrically positioned despite the fact that the object is a symmetrical sphere.

In E, the lines are directed away from a negative charge.

NUMBER 2

Erin Agin drew the following electric field lines for a configuration of two charges. What did

Erin do wrong? Explain.

SOLUTION

Electric field lines should never intersect each other. Erin crossed his lines.

NUMBER 3

. Consider the electric field lines shown in the diagram below. From the diagram, it is apparent that object A is ____ and object B is ____.

a. +, +

b. -, -

c. +, -

d. -, +

e. insufficient info

SOLUTION

: D

Electric field lines are directed towards object A so object A must be negative. They are directed away from object B so object B must be positive.

NUMBER 4

Consider the electric field lines drawn at the right for a configuration of two charges. 

Several locations are labeled on the diagram. Rank these locations in order of the electric field strength - from smallest to largest.

SOLUTION

: DAECB (with the order of C and B being in question)

Electric field strength is greatest where the lines are closest together and weakest where lines are furthest apart.