Dipole in electric field

Question

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?

Answer 1

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.