A system has two charges $q_{A}=2.5 \times 10^{-7} C$ and $q_{B}=-2.5 \times 10^{-7} C$ located at points $A$ : $(0,0,-15 \mathrm{~cm})$ and $B$ : $(0,0,+15 \mathrm{~cm})$, respectively. What are the total charge and electric dipole moment of the system?
Both the charges can be located in a coordinate frame of reference as shown in the given figure.
At $A$, amount of charge, $q_{A}=2.5 \times 10^{-7} \mathrm{C}$
At $\mathrm{B}$, amount of charge, $q_{\mathrm{B}}=-2.5 \times 10^{-7} \mathrm{C}$
Total charge of the system,
$q=q_{A}+q_{B}$
$=2.5 \times 10^{-7} \mathrm{C}-2.5 \times 10^{-7} \mathrm{C}$
= 0
Distance between two charges at points A and B,
d = 15 + 15 = 30 cm = 0.3 m
Electric dipole moment of the system is given by,
$p=q_{A} \times d=q_{B} \times d$
$=2.5 \times 10^{-7} \times 0.3$
$=7.5 \times 10^{-8} \mathrm{C}$ m along positive $z$-axis
Therefore, the electric dipole moment of the system is $7.5 \times 10^{-8} \mathrm{C} \mathrm{m}$ along positive $z$-axis.
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