# Electric field intensity and electric field lines

“The electric field is a region around a charge in which it exerts electrostatic force on another charges.”

According to coulomb’s law ,if a unit positive charge q_{0} (call it a test charge) is brought near a charge q (call a field charge) placed in space,the charge q_{0 }will experience a force.The value of this force depends upon the distance between the two charges.If the charge q_{0} is moved away from q ,this force would decrease till at a certain distance the force would be practically reduced to zero.The charge q_{0} is then out of the influence of charge q.

The region of space surrounding the charge q in which it exerts a force on the charge q_{0} is known as E.F of the charge q.Mathematically it is expressed as:

E =F/q_{0}

The direction of the vector E is the same as the direction of F,because q_{0} is a positive scalar. Dimensionally,the E.F is force per unit charge,and its SI unit is the newton/coulomb (N/C).

Note the similarity with the gravitational field,in which g (which is usually expressed in units m/sec^{2}) can also be expressed as the force per unit mass in units of newton/kilogram.Both the gravitational and electric fields can be expressed as a force divided by a property (mass or charge)of the test body.Below table of some electric fields that occurs in a few situations.

Location | Electric field (N/C) |

At the surface of a uranium nucleus | 3×10^{21} |

Within a hydrogen atom,at the electron orbit | 3×10^{11} |

Electric breakdown occur in air | 3 × 10^{6} |

At the charged drum of a photocopier | 10^{5} |

The electron beam accelerator in a TV set | 10^{5} |

Near a charged plastic comb | 10^{3} |

In the lower atmosphere | 10^{2} |

Inside the copper wire of household circuits | 10^{-2} |

## Electric field intensity

“The strength of an E.F at any point in space is known as electric field intensity.”In order to find the value of electric intensity at a point in the field,of charge +q,we place a test charge q_{0} at that point,as shown in figure

## Electric field intensity formula

If F is the force acting on the test charge q_{0},the electric field intensity would be given by:

E = F/q_{0 }………(1)

The electric field intensity at any point is defined as the force acting on a unit positive charge placed at that point.Where F is the electrostatic force between the source charge ‘q’ and the test charge ‘q_{0}‘.The test charge ‘q_{0}‘,should be very small,so that it cannot disturb the field produced by source charge ‘q’.Therefore the electric field intensity can be written as:

………….(2)

## Electric field intensity due to point charge

Consider a test charge ‘q_{0}‘ placed at point P in the electric field of a point charge ‘q’ at a distance ‘r’ apart.

We want to find out electric field intensity at point ‘p’ due to a point charge ‘q’.The electrostatic force ‘F’ between ‘q’ and ‘q_{0}‘ can be find out by using expression:

The electric field intensity ‘E’ due to a point charge ‘q’ can be obtained by putting the value of electrostatic force in equation (1).

Where r^{→ }is the unit vector which gives the direction of E.F intensity.

**Watch video about E.F:**

## Electric Field Lines

A visual representation of the electric field can be obtained in terms of electric field lines;an idea proposed by Michael Faraday.Electric field lines can be thought of a “map” that provides information about the direction and strength of the electric field at various places.As electric field lines provide information about the electric force exerted on a charge ,the lines are commonly called”lines of force”.

To introduce electric field lines ,we place positive test charges each of magnitude q0 at different places but at equal distances from a positive charge +q.

Above figure shows that each test charge will experience a repulsive force,as indicated by arrows.Therefore,the E.F created by the charge +q is directed radially outward as shown in figure below.It shows corresponding field lines which show the field direction.

.

In case of negative charge the lines are radially “inward”,because the force on a positive test charge is now of attraction,indicating the E.F points inward.

Above both figures represent two dimensional pictures of the field lines.However ,E.F lines emerge from the charges in three dimensions,and an infinite number of lines could be drawn.

The E.F lines “map” also provides information about the strength of electric field.As we noticed in above figures that field lines are closer to each other near charges where the field is strong while they continuously spread out indicating a continuous decrease the field strength.

“The number of lines per unit area passing perpendicularly through an area is proportional to the magnitude of the electric field.”

The electric field lines are curved in case of two identical separated charges in below figure.It shows the pattern of lines associated with two identical positive point charges of equal magnitude.It reveals that the lines in the region between two like charges seem to repel each other .The behaviour of identical negative charges will be exactly the same.The middle region shows the presence of a zero field spot or neutral zone.

The field lines start from positive charge and end on a negative charge.In the regions where the field lines are parallel and equally spaced ,the same number of lines pass per unit area and therefore ,field is uniform on all points.

Above figure shows the field lines between the plates of a parallel plate capacitor .The field is uniform in the middle region where field lines are equally spaced.In the central region of a parallel plate capacitor the electric field lines are parallel and evenly spaced,indicating that the electric field there has the same magnitude and direction at all points.

## Properties of electric field lines

- Electric field lines originate from positive charges and end on negative charges.
- The tangent to a field line at any point gives the direction of the electric field at that point.
- The lines are closer where the field is strong ,the lines are farther apart where the field is weak.
- No two lines cross each other .This is because field lines have only one direction.If the lines cross , field lines could have more than one direction.

You can clear more concepts about electric field lines visually in the video below.

## One Comment