AP Physics C Questions on Electric Potential due to an Electric Dipole

📚 Quick Study Guide

• ⚡ An electric dipole consists of two equal and opposite charges, $+q$ and $-q$, separated by a distance $d$.
• 📐 The dipole moment, denoted by $\vec{p}$, is a vector pointing from the negative charge to the positive charge, with magnitude $p = qd$.
• 📍 The electric potential $V$ at a point P due to an electric dipole is given by: $V = \frac{1}{4\pi\epsilon_0} \frac{p \cos\theta}{r^2}$, where $r$ is the distance from the center of the dipole to the point P, and $\theta$ is the angle between the dipole moment vector $\vec{p}$ and the position vector $\vec{r}$.
• ➕ Remember that electric potential is a scalar quantity.
• 💡 For points far away from the dipole ($r >> d$), the above formula is a good approximation.
• 🎯 The electric potential is zero at points along the perpendicular bisector of the dipole.

Practice Quiz

1. Which of the following best describes an electric dipole?
   1. A) A single positive charge.
   2. B) A single negative charge.
   3. C) Two equal and opposite charges separated by a distance.
   4. D) Two equal and like charges separated by a distance.
2. What is the direction of the electric dipole moment vector?
   1. A) From the positive charge to the negative charge.
   2. B) From the negative charge to the positive charge.
   3. C) Perpendicular to the line connecting the charges.
   4. D) Tangential to the line connecting the charges.
3. The electric potential due to a dipole at a point P is given by $V = \frac{1}{4\pi\epsilon_0} \frac{p \cos\theta}{r^2}$. What does $\theta$ represent?
   1. A) The angle between the line connecting the charges and the x-axis.
   2. B) The angle between the dipole moment vector and the position vector.
   3. C) The angle between the position vector and the x-axis.
   4. D) The angle between the dipole moment vector and the y-axis.
4. At what location(s) is the electric potential due to a dipole approximately zero?
   1. A) Along the line connecting the two charges.
   2. B) Along the perpendicular bisector of the dipole.
   3. C) At a large distance from the dipole, regardless of direction.
   4. D) Both B and C.
5. If the charge of a dipole is doubled and the separation distance is halved, what happens to the dipole moment?
   1. A) It remains the same.
   2. B) It doubles.
   3. C) It quadruples.
   4. D) It is halved.
6. Which of the following factors does NOT affect the electric potential due to an electric dipole at a given point?
   1. A) Magnitude of the charge.
   2. B) Separation distance between the charges.
   3. C) Permittivity of free space.
   4. D) Mass of the charges.
7. An electric dipole is placed in a uniform electric field. What is the net force on the dipole?
   1. A) Always zero.
   2. B) Depends on the orientation of the dipole.
   3. C) Proportional to the electric field strength.
   4. D) Proportional to the dipole moment.