# Torque on a dipole in an electric field

• castrodisastro
In summary, The torque exerted on the electric dipole by the uniform electric field can be calculated by taking the cross product of the dipole moment and the magnitude of the electric field, multiplied by the sine of the angle between them. This results in a torque of 3.44*10-14N*m, which may differ from the expected answer due to rounding errors.
castrodisastro

## Homework Statement

An electric dipole has opposite charges of 6.55⋅10−15C separated by a distance of 0.65mm. It is oriented at 54.0° with respect to a uniform electric field of magnitude 10.0⋅103N/C. Determine the magnitude of the torque exerted on the dipole by the electric field.

q+=6.55*10-15C
q-=-6.55*10-15C
r=0.00065m
$\vec{E}$=10,000N/C
Θ=54.0°

## Homework Equations

p=qd
$\tau$=p$\times$$\vec{E}$

## The Attempt at a Solution

The angle of the dipole is 54.0° with respect to the uniform electric field. Using trig I can see that the torque can be calculated by the cross product of the dipole moment and the magnitude of the electric field multiplied by sin(Θ).

$\tau$=p$\times$$\vec{E}$

The dipole moment is given by charge times the distance(r)

p=qd

p=(6.55*10-15C)(0.00065m)=4.26*10-18C*m

If we plug in that value into our torque equation...

$\tau$=p$\times$$\vec{E}$sin(Θ)

$\tau$=(4.26*10-18C*m)*(10,000N/C)*sin(54°)

$\tau$=3.44*10-14N*m

Which is not correct according to my online homework. This calculation seems simple...too simple. Am I missing something?

Also, if the torque results from a cross product operation, which is an operation between vectors, then in this case I just multiply the magnitude of the dipole moment and the magnitude of the electric field because we are not working with vectors in this problem?

As always, any help is appreciated. Thanks in advance.

castrodisastro said:
$\tau$=3.44*10-14N*m
I get the same.
Also, if the torque results from a cross product operation, which is an operation between vectors, then in this case I just multiply the magnitude of the dipole moment and the magnitude of the electric field because we are not working with vectors in this problem?
No, you must include the sin(). Is that what you meant?

## 1. What is torque on a dipole in an electric field?

Torque on a dipole in an electric field is the rotational force experienced by a dipole (a pair of opposite charges separated by a distance) when placed in an electric field (a region where electrically charged particles experience a force).

## 2. How is torque on a dipole in an electric field calculated?

The magnitude of torque on a dipole in an electric field is equal to the product of the electric field strength and the dipole moment (the product of the magnitude of the charges and the distance between them). The direction of the torque is perpendicular to both the electric field and the dipole moment.

## 3. What factors affect the torque on a dipole in an electric field?

The magnitude of the electric field, the magnitude of the dipole moment, and the angle between the electric field and the dipole moment all affect the torque on a dipole in an electric field. A stronger electric field or a larger dipole moment will result in a larger torque, while a smaller angle between the electric field and the dipole moment will result in a larger torque.

## 4. What is the significance of torque on a dipole in an electric field?

The torque on a dipole in an electric field is important in understanding the behavior of electric dipoles in various systems, such as in electronic devices or molecules. It also plays a role in the movement and alignment of particles in electric fields, which can be useful in applications such as particle manipulation and separation.

## 5. Can the torque on a dipole in an electric field be zero?

Yes, the torque on a dipole in an electric field can be zero if the electric field and the dipole moment are parallel or antiparallel to each other. In this case, the dipole experiences a force but does not undergo any rotational motion.

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