Question

Find dipole moment of a system consisting of charge \(q_1 = 3\,\mu C\) and \(q_2 = -9\,\mu C\) with position coordinates \(\vec r_1 = 2\hat i + 3\hat j + 3\hat k\) and \(\vec r_2 = \hat i + \hat j + \hat k\) respectively.

• A. \(-3\hat i\ \mu C\text{-m}\)
• B. \(-9\hat i\ \mu C\text{-m}\)
• C. \(-6\hat i\ \mu C\text{-m}\)
• D. \(-5\hat i\ \mu C\text{-m}\)

Answer 1

The Correct Option is A

Concept: The electric dipole moment of a system of charges is given by \[ \vec p = \sum q_i \vec r_i \] where \(q_i\) = charge \(\vec r_i\) = position vector of charge
Step 1:Write the given quantities. \[ q_1 = 3\,\mu C \] \[ q_2 = -9\,\mu C \] \[ \vec r_1 = 2\hat i + 3\hat j + 3\hat k \] \[ \vec r_2 = \hat i + \hat j + \hat k \]
Step 2:Use the dipole moment formula. \[ \vec p = q_1 \vec r_1 + q_2 \vec r_2 \]
Step 3:Substitute the values. \[ \vec p = 3(2\hat i + 3\hat j + 3\hat k) - 9(\hat i + \hat j + \hat k) \] \[ \vec p = (6\hat i + 9\hat j + 9\hat k) - (9\hat i + 9\hat j + 9\hat k) \] \[ \vec p = -3\hat i \] \[ \boxed{\vec p = -3\hat i\ \mu C\text{-m}} \]