Dipole in an Uniform Electric Field:

[fallen186]

Dipole in an Uniform Electric Field:
torque is calculated about the position of either charge has the magnitude FLsin(x) = qELsin(x) = pEsin(x). The direction of the torque vector is into the paper such that it tends to rotate the dipole moment vector p so it aligns with the direction of E. The torque can be expressed most concisely as the cross product: T = p x E

I don't know why the magnitude is F * L sin(x) or why qE turns into pE. And I don't understand what the concept iit s trying to tell me. It would also be helpful if someone could explain the hand thing for torque. I understand most of the stuff about torque but not the hand thing.

x = theta
L = distance between charges in dipole
p = vector of the dipole movement that points from negtive charge to positive.
p =q*L

 

[Born2bwire]

The dipole moment is defined as being L*q, so qELsin(x) = pEsin(x) by definition. As for F*L*sin(x), that's simply the scalar form of the vector cross product of F x L. Torque is defined as the cross product between the force vector and the vector denoting the lever arm. To find the torque on a dipole, they fix one of the charges as the center of rotation (or choose the midpoint, the result is the same since the magnitude of the force is the same) and assume that the length between the charges (or the dipole moment) to be the lever arm. The force is the Lorentz force resulting from the electric field.

I think you should brush up on torque and vectors because these are very basic concepts.

 

[astrokreng]

Hello there,

I can explain the concept of torque and its relation to a dipole in an uniform electric field. Torque is a force that causes rotation or twisting, and it is calculated by multiplying the force applied by the distance from the pivot point. In this case, the pivot point is the position of either charge in the dipole.

When a dipole is placed in an uniform electric field, it experiences a torque due to the interaction between the charges and the electric field. This torque is calculated as FLsin(x), where F is the force applied, L is the distance between the charges in the dipole, and x is the angle between the force and the dipole moment vector p. The dipole moment vector p is a vector that represents the strength and direction of the dipole, and it points from the negative charge to the positive charge.

In the equation, qE is used to represent the force applied on the dipole due to the electric field. This is because the electric field exerts a force on the charges in the dipole, causing them to experience an opposite force and creating a torque. The magnitude of this force is equal to qE, where q is the charge of the dipole and E is the strength of the electric field.

The direction of the torque vector is into the paper, which means it is perpendicular to the plane of the dipole and the electric field. This torque tends to rotate the dipole moment vector p so that it aligns with the direction of the electric field. This can be seen by imagining a hand turning a screwdriver. The hand represents the torque vector and the screwdriver represents the dipole moment vector. The hand turning the screwdriver causes it to rotate and align with the direction of the force.

In summary, the equation for torque in a dipole in an uniform electric field is T = p x E, where p is the dipole moment vector and E is the strength of the electric field. This equation represents the interaction between the charges in the dipole and the electric field, and how it causes the dipole to rotate and align with the electric field. I hope this explanation helps clarify the concept for you.