Question

Two charges $+q$ and $-q$ are placed at a distance $b$ apart as shown in the figure.
The electric field at a point $P$ on the perpendicular bisector is shown as :

• A. Along vector $\overrightarrow{A}$
• B. Along vector $\overrightarrow{B}$
• C. Along vector $\overrightarrow{C}$
• D. Zero

Answer 1

Answer: (A)

Answer is A.

An electric dipole is made of two equal and opposite charges that are a distance d away. Any molecule that has its center of positive charges away from its center negative charges forms a dipole.
In this case, we have a dipole and to determine the electric field which result from the dipole charges in Figure that are separated by a distance b, we simply sum the fields from each charge individually. Note that the fields are vectors.
$\overrightarrow{E}=\overrightarrow{E_{1x}}+\overrightarrow{E_{2x}}$.
The magnitude of the electric field (E1) due to the first charge (q1) and the magnitude of the electric field (E2) due to the second charge (q2) are the same although the directions are different.
The components of the electric field along the x axis $\overrightarrow{E_{1x}}and\overrightarrow{E_{2x}}$ have the same magnitude but opposite directions and cancel each other out.
So, the resultant electric field is along the vector E, that is vector A as given in the figure.