A system has two charges qA = 2.5 × 10−7 C and qB = −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?

Question 1.9: 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?

Answer: 

Method - 1

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 × 10⁻⁷C

At B, amount of charge, q_B = −2.5 × 10⁻⁷ C

Total charge of the system,

q = q_A + q_B

= 2.5 × 10⁷ C − 2.5 × 10⁻⁷ 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 × d = q_B × d

2.5 × 10⁻⁷ × 0.3

7.5 × 10⁻⁸ C m along positive z-axis

Therefore, the electric dipole moment of the system is 7.5 × 10⁻⁸ C m along positive z−axis.

Method - 2