Electric field lines and flux

Electric field lines

Electric field lines are examined by using a unit positive charge

For a +ve charge the electric field lines are radially outward

For a -ve charge the electric field lines are radially inward

Electric field lines due to two positive charges

Electric field lines due to two positive and negative charges

For two positive and negative charges electric field line starts from the positive charge and ends at the negative charge.

Dipole: if the two charges are equal and opposite then they are called dipole.

Be remember:

1)Electric field lines can not be drawn in a 2-D paper, it is a 3-dimensional concept in space.

2)Two electric field lines never intersect each other. This is because if two electric field lines intersect at a point then there will be two directions at the same point which is impossible. Electric field intensity has one and only one direction, can not have two or more direction at the same point.

3)the no of electric field lines crossing perpendicular per unit area is called the electric field intensity at that point.

4)in space or three-dimensions solid angle is used to define a cone. For a particular cone angle the no of electric field lines is constant everywhere.

Suppose is the cone angle or solid angle

5)We know that

[ where r₁ is the perpendicular distance of the area A from O ]

Since the cone angle or solid angle is also same for area B, then

Therefore density or number of electrical field lines per unit area is [for area A]

[ where n is the no of electric field lines passing through the area ]

Since n is constant for a particular solid angle

So,

Similarly we can also prove that

6) The no of electric field lines crossing per unit area (in perpendicular) is called the density or the electric field strength. At that position.

As you can see A & B are two cross-section having same area, that is

Area A = Area B

But the no of field lines crossing in area A is more than the area B,

So electric field strength is area A is more and electric field strength in area B is weak.

Electric flux

1) Electric flux is denoted as

2) Electric flux is the no of electric field lines crossing through a surface perpendicularly. [not necessarily a unit area surface, it may be very large or very small surface also]

3) Suppose a surface is perpendicular to the electric field and have area , then the electric flux is