Chapter 33, Problem 21A

The diagrams A, B, and C represent pairs of charges in three different arrangements. The distance from point P to the nearest charge is the same in each arrangement. Rank the arrangements A, B, and C from strongest to weakest electric field at point P.

To determine

To rank: The arrangements A, B, C from strongest to weakest electric field at point P.

Answer to Problem 21A

  $C>B>A$

Explanation of Solution

Introduction:

A force field that is surrounding an electric charge or a group of charges can be defined as an electric field. Mathematically, the electric field strength is given as:

  $E=\frac{F}{q}$

Hence, the electric field is strongest when the force is greatest and vice versa.

At point A, the same negative charges cancel out the electric field on point P as the point is in the middle of two like charges. Hence, the electric field is weakest at this point. Similarly, at point C, the electric field is doubled because the point P now lies in the middle of two opposite or unlike charges. So, the electric field is strongest in this case. But, in case of point B, both the charges are at one end from the point P due to which the electric field will be weaker.

Hence, the ranking for the three cases will be: $C>B>A$

Conclusion:

Hence, the arrangements A, B, C are ranked as $C>B>A$