# Chapter 16 - Problems - Page 618: 84

The electric field due to the two point charges is zero at one point in region A.

#### Work Step by Step

In region A, the electric fields due to the $+2~\mu C$ point charge and the $-4~\mu C$ point charge are non-zero and they point in opposite directions. The net electric field is zero when the magnitude of the electric field due to each point charge is equal. In region B, the electric fields due to the $+2~\mu C$ point charge and the $-4~\mu C$ point charge are non-zero and they point in the same direction. Therefore, the net electric field is non-zero in this region. In region C, the electric fields due to the $+2~\mu C$ point charge and the $-4~\mu C$ point charge are non-zero and they point in opposite directions. However, for every point in this region, the distance to the $-4~\mu C$ charge is less than the distance to the $+2~\mu C$ charge. Therefore, the magnitude of the electric field due to the $-4~\mu C$ charge is always greater than the magnitude of the electric field due to the $+2~\mu C$ charge. The net electric field is non-zero in this region. The electric field due to the two point charges is zero at one point in region A.

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