# Dipole in electric field

An electric dipole is placed in a uniform electric field at some angle, say 90 degrees. The dipole consists of 2 charges, one negative and one positive. The charge which is positive will have a torque which is in the direction of the field and the negative charge will have a torque opposite to the direction of the field. Now my question is what determines the direction of torques. Why is the direction of torque due to negative charge opposite to the direction of electric field ? Why can't it be in the same direction like the positive charge?

Also, if the dipole is placed in a non-uniform field, how do we determine the direction of the force acting on the negative and positive charges of dipole?

• Hello, and welcome to Physics SE. Look around, and take the tour. For this question, I would suggest sketching it out and looking at how the field interacts with the differently charged particles. – Jon Custer Mar 30 '16 at 14:23

You may be confusing torque and force. The force $\vec{\mathrm{F}}$ is given by $q\, \vec{\mathrm{E}}$, so you can clearly see that the force is in different directions for the positive and negative charges, and is either parallel or antiparallel to the electric field.

The torque $\vec{\tau}$ about any point $O$ is given by $\vec{\mathrm{r}} \times \vec{\mathrm{F}}$, where $\vec{\mathrm{r}}$ is the displacement of the charge from $O$. $\vec{\tau}$ points out of the plane defined by $\vec{\mathrm{r}}$ and $\vec{\mathrm{F}}$ (or equivalently $\vec{\mathrm{r}}$ and $\vec{\mathrm{E}}$).

If $O$ is the midpoint of the dipole, then $\vec{\mathrm{r}}_1 = -\vec{\mathrm{r}}_2$, and since $q_1 = - q_2$, then $\vec{\mathrm{F}}_1 = - \vec{\mathrm{F}}_2$, therefore $\vec{\mathrm{\tau}}_1 = \vec{\mathrm{\tau}}_2$.

So the torques are in the same direction for both of the charges.

For a non-uniform electric field, the direction of the force on a charge will be either parallel or anti-parallel to the local direction of the electric field, depending on the sign of the charge.

• Good answer; it would benefit from a diagram. And while we discourage "multiple" questions, it might be worth addressing the "Also, if..." last paragraph of the question? – Floris Mar 30 '16 at 13:35
• @Floris, it's true about the diagram, but that stretches beyond my lunch hour ;). I believe that I've addressed the last paragraph of the question in the first paragraph of mine. – Gremlin Mar 30 '16 at 13:38
• You don't address the "non-uniform" part... either way you got my upvote. – Floris Mar 30 '16 at 13:39
• @Floris Oh, missed that crucial word. Good catch. – Gremlin Mar 30 '16 at 13:41