Chapter 16, Problem 21Q

Show, using the three rules for field lines given in Section 16—8, that the electric field lines starting or ending on a single point charge must be symmetrically spaced around the charge.

To determine

To show that the electric field lines starting or ending on a single point charge is symmetrically spaced around the charge.

Answer to Problem 21Q

Solution:

It is shown that the electric field lines starting or ending on a single point charge is symmetrically spaced around the charge.

Explanation of Solution

The three rules for electric field lines are,

1)Electric field lines start from positive charges and end at negative charges. If there is a single charge, they may start or end at infinity.

2)The tangent drawn to a line of force at a point is in the direction of electric field at that point.

3)The number of field lines crossing unit area normal to the lines of force is equal to the magnitude of electric field intensity at that point.

The electric field lines due to a single positive charge and a single negative charge are given by,

So, from the above two figures we can conclude that the electric field lines starting or ending on a single point charge is symmetrically spaced around the charge.