AP Physics C: Electricity and Magnetism Questions on Electric Dipoles

📚 Quick Study Guide

• ⚡ Electric Dipole: A separation of positive and negative charges. Often modeled as two equal and opposite charges (+q and -q) separated by a distance d.
• 📏 Dipole Moment (p): A vector quantity pointing from the negative charge to the positive charge. Magnitude is given by $p = qd$. Units are Coulomb-meters (C·m).
• 🧮 Electric Potential (V) due to a Dipole: At a point P located a distance r from the center of the dipole and at an angle $\theta$ with respect to the dipole axis: $V = \frac{1}{4\pi\epsilon_0} \frac{p \cos{\theta}}{r^2}$, where $\epsilon_0$ is the permittivity of free space.
• 💪 Electric Field (E) due to a Dipole: The electric field can be calculated by taking the gradient of the electric potential. Close to the dipole and along its axis, $E \approx \frac{1}{2\pi\epsilon_0} \frac{p}{r^3}$. Perpendicular to the axis, $E \approx \frac{1}{4\pi\epsilon_0} \frac{p}{r^3}$.
• 🌀 Torque on a Dipole in an Electric Field: When a dipole is placed in a uniform external electric field (E), it experiences a torque given by $\tau = pE \sin{\theta}$, where $\theta$ is the angle between p and E. In vector form: $\vec{\tau} = \vec{p} \times \vec{E}$.
• 📈 Potential Energy (U) of a Dipole in an Electric Field: $U = -\vec{p} \cdot \vec{E} = -pE \cos{\theta}$. The potential energy is minimum when the dipole is aligned with the electric field ($\theta = 0$).

Practice Quiz

1. Which of the following defines the dipole moment?
   1. A) The sum of two equal charges
   2. B) The product of charge and the distance between charges
   3. C) The difference between two opposite charges
   4. D) The ratio of charge to the distance between charges
2. What is the direction of the dipole moment vector?
   1. A) From positive to negative charge
   2. B) From negative to positive charge
   3. C) Parallel to the electric field
   4. D) Perpendicular to the electric field
3. The electric potential due to a dipole at a large distance $r$ varies as:
   1. A) $1/r$
   2. B) $1/r^2$
   3. C) $1/r^3$
   4. D) $1/r^4$
4. What is the torque on an electric dipole when it is aligned parallel to the electric field?
   1. A) Maximum
   2. B) Minimum
   3. C) Undefined
   4. D) Constant
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 degrees
   2. B) 90 degrees
   3. C) 180 degrees
   4. D) 270 degrees
6. An electric dipole is placed in a uniform electric field. Which of the following statements is true?
   1. A) It always experiences a net force.
   2. B) It always experiences a torque.
   3. C) It experiences a net force only if the field is non-uniform.
   4. D) It experiences a torque only if it is aligned with the field.
7. If the charge on each dipole is doubled and the distance between them is halved, what happens to the dipole moment?
   1. A) It remains the same.
   2. B) It is doubled.
   3. C) It is halved.
   4. D) It is quadrupled.