>[!summary] A dipole is any arrangement of two equal charges but opposite signs. The field lines always point from positive to negative charge. > A dipole in an electric field will experience a torque along with a force from the electric field. If a torque is produced, there will be a potential energy created depending on the direction of the torque. > **Key equations:** > Dipole moment: $p = qd$ > Torque on dipole: $\tau = pE sin(\theta)$ > Potential energy: $U = -p \cdot E$ >[!info]+ Read Time **⏱ 3 mins** # Definition A dipole is any arrangement of two equal in magnitude but opposite sign [[Charge]]. **The field lines always point from a + charge to a - charge.** ![[dip_2.png | 400]] [^1] >[!note] Explanation Example of a dipole We define a dipole moment as the amount of force in-between the two charges. Mathematically, we define this as the distance between two charges, and the charge. $ p = qd $ # Torque on Dipoles When you place a dipole in an electric field, the field produces a force on both parts of the dipole. That force will cancel each other, but the [[Moment of Inertia#Torque|torque]] will add up. >[!warning] Assumptions Recall that [[Moment of Inertia#Torque|torque]] is the defined by the [[! Cross Product|cross product]] of force and distance $ \begin{array}{c} \tau = \vec{p} \times \vec{E} \\ \tau = pE sin(\theta) \end{array} $ ![[dip_1.png]] [^1] >[!note] Explanation A dipole in an electric field exerts. The force produced by the electric field is cancelled out # Potential Energy of A Dipole >[!warning] Assumption If there is a [[Moment of Inertia#Torque|torque]] on the dipole, then there must be some [[Electric Potential Energy|potential energy]] of the dipole. > The [[Electric Potential Energy|potential energy]] of a dipole is found from the argument that $\Delta U = -W$ and that $dW = \tau d\phi$ We integrate to find the [[Work#Work|work]] needed, and our potential energy will be the negative of work because in order to decrease the potential energy, negative work must be done (it naturally will do this) $W = \int dW = \int_{\phi_1} ^ {\phi_2} pEsin\theta d\phi= pE(cos\phi _1 - cos\phi _2)$ so: $\begin {array} {c} U = -pE cos(\theta)\\ U = -p \cdot E \end{array}$ >[!bug] Special Note In order to get higher potential energy you have to do work on the object, which is not naturally done. And lower the potential energy is naturally done. > Also notice that our potential energy is the [[Dots Product & Angles|dot product]] of $p$ and $E$ which is most commonly how its formatted # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/UFqTFhoS0sM?si=Bje7NYKoCaWc8GL9" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe> --- > 🧠 Enjoy this walkthrough? [Support Math & Matter](https://github.com/rajeevphysics/Obsidan-MathMatter) with a star and help others learn more easily. --- [^1]: Taken from https://tikz.net/electric_dipole/ by Izaak Neutelings (July 2018)