# Calculating Energy, Force, and Torque of a Dipole in a Point Charge Field

• apw235
In summary, the problem involves a dipole located a distance d above a point charge q, with the dipole aligned in either the z or y direction. The goal is to calculate the energy, force, and torque of the dipole in the field of the charge. The equations used are U=-\vec{P}\bullet\vec{E} for energy and \tau=\vec{P}\times\vec{E} for torque. For the y direction alignment, the torque is 0, but more information is needed to solve the problem. The solution likely involves the electric field of the point charge and the dipole moment. Any further help or hints would be appreciated.
apw235

## Homework Statement

A dipole sits a distance d above a point charge q which is located at the origin of our coordinate system. In (a) it is aligned in the z direction and in (b) in the y direction. Calculate the energy, force, and torque of the dipole in the field of the charge.
(see attachment)

## Homework Equations

U=-$$\vec{P}\bullet\vec{E}$$ Energy
$$\tau=\vec{P}\times\vec{E}$$ Torque

## The Attempt at a Solution

For (b) it is clear that the Torque is 0, but that is about all I've figured out so far...

#### Attachments

• Untitled1.png
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I am not sure how to approach this problem, but I believe it has something to do with the electric field of the point charge and the dipole moment.Any help/hints would be greatly appreciated!

I would approach this problem by first identifying the variables and parameters involved. In this case, we have a dipole with a charge of q, located at a distance d from a point charge also with a charge of q. The dipole is oriented in either the z or y direction.

Next, I would use the given equations for energy and torque to calculate the values for each orientation. For the energy, we can use the equation U=-\vec{P}\bullet\vec{E}, where \vec{P} is the dipole moment and \vec{E} is the electric field. In this case, the electric field can be calculated using Coulomb's Law, \vec{E}=\frac{q}{4\pi\epsilon_0}\frac{\vec{r}}{r^3}, where \vec{r} is the distance vector from the point charge to the dipole.

For the torque, we can use the equation \tau=\vec{P}\times\vec{E}, where \times represents the cross product. Again, we can use Coulomb's Law to calculate the electric field, and the dipole moment can be calculated as \vec{P}=q\vec{d}, where \vec{d} is the vector pointing from the negative to positive charge of the dipole.

Once we have calculated the energy and torque for both orientations, we can compare the values to see how they differ. For example, in (a) when the dipole is aligned in the z direction, the energy will be maximized because the dipole moment is parallel to the electric field, resulting in a dot product of 1. In contrast, when the dipole is aligned in the y direction, the energy will be minimized because the dipole moment is perpendicular to the electric field, resulting in a dot product of 0.

Similarly, in (b) when the dipole is aligned in the y direction, the torque will be maximized because the dipole moment is perpendicular to the electric field, resulting in a cross product of the magnitude of the dipole moment and the magnitude of the electric field. In contrast, when the dipole is aligned in the z direction, the torque will be minimized because the dipole moment is parallel to the electric field, resulting in a cross product of 0.

In conclusion, by using the given equations and the principles of Coulomb's

## 1. How do you calculate the energy of a dipole in a point charge field?

To calculate the energy of a dipole in a point charge field, you can use the equation U = -pEcosθ, where U is the energy, p is the magnitude of the dipole moment, E is the electric field, and θ is the angle between the dipole moment and the electric field.

## 2. What is the formula for calculating the force on a dipole in a point charge field?

The formula for calculating the force on a dipole in a point charge field is F = pEsinθ, where F is the force, p is the magnitude of the dipole moment, E is the electric field, and θ is the angle between the dipole moment and the electric field.

## 3. How do you find the torque on a dipole in a point charge field?

To find the torque on a dipole in a point charge field, you can use the equation τ = pEsinθ, where τ is the torque, p is the magnitude of the dipole moment, E is the electric field, and θ is the angle between the dipole moment and the electric field.

## 4. What is the relationship between the dipole moment and the electric field in a point charge field?

The relationship between the dipole moment and the electric field in a point charge field is given by the equation p = qd, where p is the dipole moment, q is the magnitude of the charge on each end of the dipole, and d is the distance between the charges.

## 5. How does the angle between the dipole moment and the electric field affect the energy and force on a dipole in a point charge field?

The angle between the dipole moment and the electric field affects the energy and force on a dipole in a point charge field by changing the amount of work done by the electric field on the dipole. When the angle is 0 or 180 degrees, the energy and force are maximized, while at 90 degrees, they are minimized. This is due to the cosine and sine functions in the equations for energy and force, respectively.

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