Dipole in an external electric field

In summary, the conversation discusses the expression for torque on a dipole in an external electric field, specifically the order of the vectors in the cross product. It is noted that there is no indication in the derivations that it must be PxE, and the possibility of ExP is questioned. It is also mentioned that the direction of the resultant is opposite for A x B and B x A, and this is attributed to the definitions of positive and negative directions in the chosen coordinate system.
  • #1
Prashasti
63
2

Homework Statement


Why isn't the expression for torque on a dipole kept in an external electric field ExP? Why is it PxE?
No such indication has been given in any of the derivations, that it is mandatory for it to be PxE, so why can't it be ExP?

2. The attempt at a solution
Is it all about experiments?
 
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  • #2
Prashasti said:

Homework Statement


Why isn't the expression for torque on a dipole kept in an external electric field ExP? Why is it PxE?
No such indication has been given in any of the derivations, that it is mandatory for it to be PxE, so why can't it be ExP?

2. The attempt at a solution
Is it all about experiments?
What's the essential difference in the cross products A x B versus B x A?
 
  • #3
The direction of the resultant of A x B is just opposite to that of B x A...
 
  • #4
Prashasti said:
The direction of the resultant of A x B is just opposite to that of B x A...
Right. So it comes down to the definitions of positive or negative directions for quantities in the chosen coordinate system. This includes assumed directions for positive or negative torques, angular velocities, etc., which are vector quantities (or pseudo vector quantities in some cases, but that's another topic).
 
  • #5

The expression for torque on a dipole in an external electric field is given by the cross product of the dipole moment vector (P) and the electric field vector (E). This is because the torque experienced by a dipole is perpendicular to both the dipole moment and the electric field. Therefore, it is mathematically correct to write the expression as PxE.

However, it is important to note that the order of the vectors in a cross product does not affect the magnitude of the resulting vector. In other words, the magnitude of PxE is the same as ExP. Therefore, both expressions are valid and can be used interchangeably.

The reason for using PxE instead of ExP may vary depending on the context. It could be due to the direction of the electric field or the orientation of the dipole moment. Ultimately, the choice of which expression to use may depend on the specific problem being studied.

In summary, the expression for torque on a dipole in an external electric field can be written as PxE or ExP, as they are mathematically equivalent. It is not mandatory for it to be written in a specific order, and the choice may depend on the context or the problem at hand.
 

FAQ: Dipole in an external electric field

What is a dipole in an external electric field?

A dipole in an external electric field refers to a pair of equal and opposite charges separated by a distance. This creates a dipole moment, which is a vector pointing from the negative charge to the positive charge. When placed in an external electric field, the dipole will experience a torque and align itself with the field.

How does an external electric field affect a dipole?

An external electric field exerts a force on each of the charges in the dipole, causing them to experience opposite forces. This creates a torque that causes the dipole to rotate until it is aligned with the field. The strength of the field and the orientation of the dipole determine the magnitude and direction of the torque.

What is meant by "polarization" in relation to a dipole in an external electric field?

Polarization refers to the separation of positive and negative charges within a material due to the influence of an external electric field. When a material contains dipoles, the external field can cause the dipoles to align, resulting in a net polarization of the material in the direction of the field.

How is the electric potential energy of a dipole in an external electric field affected?

The electric potential energy of a dipole in an external electric field is decreased when the dipole aligns with the field. This is because the dipole experiences a torque that causes it to rotate to a position of lower energy. The potential energy is also affected by the strength of the external field and the orientation of the dipole.

Can a dipole in an external electric field experience translational motion?

Yes, a dipole in an external electric field can experience translational motion if the external field is non-uniform. In a uniform field, the dipole will only experience rotational motion. However, in a non-uniform field, the forces on the two charges will not cancel out, causing a net force on the dipole. This can result in translational motion of the dipole.

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