Electric Dipole Moment Formula: Calculation and Examples

📚 Quick Study Guide

• ⚛️ An electric dipole consists of two equal and opposite charges, $+q$ and $-q$, separated by a distance $d$.
• 📏 The electric dipole moment, denoted by $\vec{p}$, is a vector quantity that points from the negative charge to the positive charge.
• 📐 The magnitude of the electric dipole moment is given by: $p = qd$
• ⚡ The SI unit of electric dipole moment is Coulomb-meter (C⋅m).
• 🧲 The electric field due to a dipole varies with distance $r$ as $\frac{1}{r^3}$, unlike the electric field due to a single charge which varies as $\frac{1}{r^2}$.
• 🔄 The torque on an electric dipole in a uniform electric field $\vec{E}$ is given by: $\vec{\tau} = \vec{p} \times \vec{E}$ and its magnitude is $\tau = pE \sin(\theta)$, where $\theta$ is the angle between $\vec{p}$ and $\vec{E}$.
• 💡 The potential energy $U$ of an electric dipole in a uniform electric field is given by: $U = -\vec{p} \cdot \vec{E} = -pE \cos(\theta)$.

🧪 Practice Quiz

1. What is the formula for the magnitude of the electric dipole moment?
   1. A. $p = \frac{q}{d}$
   2. B. $p = q + d$
   3. C. $p = qd$
   4. D. $p = \frac{d}{q}$


2. What is the SI unit of the electric dipole moment?
   1. A. Coulomb/meter (C/m)
   2. B. Coulomb-meter (C⋅m)
   3. C. Coulomb-meter squared (C⋅m²)
   4. D. Coulomb/meter squared (C/m²)


3. An electric dipole consists of charges $\pm 5 \times 10^{-6}$ C separated by a distance of 2 mm. What is the dipole moment?
   1. A. $1 \times 10^{-9}$ C⋅m
   2. B. $1 \times 10^{-8}$ C⋅m
   3. C. $1 \times 10^{-7}$ C⋅m
   4. D. $1 \times 10^{-6}$ C⋅m


4. The torque on an electric dipole in a uniform electric field is maximum when the angle between the dipole moment and the electric field is:
   1. A. 0°
   2. B. 45°
   3. C. 90°
   4. D. 180°


5. The potential energy of an electric dipole is minimum when the angle between the dipole moment and the electric field is:
   1. A. 0°
   2. B. 45°
   3. C. 90°
   4. D. 180°


6. How does the electric field due to a dipole vary with distance $r$ at large distances?
   1. A. $\frac{1}{r}$
   2. B. $\frac{1}{r^2}$
   3. C. $\frac{1}{r^3}$
   4. D. $\frac{1}{r^4}$


7. What does the electric dipole moment vector point from?
   1. A. Positive charge to negative charge
   2. B. Negative charge to positive charge
   3. C. Higher potential to lower potential
   4. D. Lower potential to higher potential