What are the Total Charge and Electric Dipole Moment of the System? Exercise Chapter 1 Exercise Chapter 1 Electric

Question 9: A system has two charges q_A = 2.5 × 10⁻⁷ C and q_B = −2.5 × 10⁻⁷ C located at points A: (0, 0, − 15 cm) and B: (0, 0, + 15 cm), respectively. What are the total charge and electric dipole moment of the system?
Solution:
Given that
q_A = 2.5 × 10⁻⁷ C
q_B = −2.5 × 10⁻⁷ C
A: (0, 0, − 15 cm)
B: (0, 0, + 15 cm),
The value of x and y coordinate is zero in both points A and B
So both points are in straight line
And the distance between both points is  = 15 – (-15) = 30 cm = 0.30 m
Total charge of the system will
q = q_A + q_B
= 2.5 × 10⁷ C − 2.5 × 10⁻⁷ C
= 0

The formula of electric dipole moment of the system
p  = charge × d
= q_A × d
= 2.5 × 10⁻⁷ × 0.3
= 7.5 × 10⁻⁸ C m

In this problem negative charge is along positive z-axis
Answer
7.5 × 10⁻⁸ C m along positive z−axis.