Question:
A system has two charge s \(q_A = 2.5 × 10^{−7} C\) 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?
A system has two charge s \(q_A = 2.5 × 10^{−7} C\) 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?
Updated On: Sep 26, 2023
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Solution and Explanation
Both the charges can be located in a coordinate frame of reference as shown in the given figure.
At A, amount of charge,\(q_A = 2.5 × 10^{−7}C\)
At B, amount of charge,\(q_B = −2.5 × 10^{−7} C\)
Total charge of the system, \(q = q_A + q_B = 2.5 × 10^7 C − 2.5 × 10^{ −7} C = 0\)
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.
At A, amount of charge,\(q_A = 2.5 × 10^{−7}C\)
At B, amount of charge,\(q_B = −2.5 × 10^{−7} C\)
Total charge of the system, \(q = q_A + q_B = 2.5 × 10^7 C − 2.5 × 10^{ −7} C = 0\)
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.
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