The magnetic forces on a magnetic dipole result in a torque...

The magnetic forces on a magnetic dipole result in a torque that tends to make the dipole line up with the magnetic field. In this problem we show that the electric forces on an electric dipole result in a torque that tends to make the electric dipole line up with the electric field. (a) For each orientation of the dipole shown in the diagram, sketch the electric forces and determine the direction of the torque- clockwise or counterclockwise - about an axis perpendicular to the page through the center of the dipole. (b) The torque always tends to make the dipole rotate toward what orientation?

Key Concepts

Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a distance, characterized by a dipole moment vector that points from the negative to the positive charge. This concept is fundamental in understanding how non-uniform charge distributions interact with an electric field, leading to forces and torques that affect their orientation.

Electric Field

An electric field is a vector field representing the force per unit charge that would be exerted on a positive test charge at any point in space. Its uniformity or variation plays a crucial role in determining the behavior and interaction of electric dipoles with the field.

Torque on an Electric Dipole

The torque experienced by an electric dipole in an electric field results from the pair of equal and opposite forces acting on the charges. Mathematically expressed as the cross product of the dipole moment and the electric field (? = p × E), this torque tends to rotate the dipole so that it aligns with the electric field.

Potential Energy of an Electric Dipole

The potential energy associated with an electric dipole in an electric field depends on its orientation relative to the field direction. The energy is minimized when the dipole moment aligns with the electric field, which explains the natural tendency of the system to rotate and align with the field in order to reach a lower energy state.

Transcript

00:01 So for part a, we want to know the direction of the torque based on the different orientations of the dipole as shown in the diagram.

00:09 So the first orientation is if your dipole is just completely horizontal and if your electric field is going to the right.

00:22 And i'm going to omit drawing the other lines here just to make it super clear.

00:26 And you will have to remember that the force, the electric field, force experienced by the positive charge will always be in the direction of the electric field, whereas the electric force as experienced by the negative charge will be in the direction opposite to the direction of the electric field.

00:45 So what that means is for this positive charge right here, you're going to experience a right word electric field, electric force, excuse me, and the negative charge right here will experience a left word electric force.

01:02 And, because they are going to be the same magnitude because the question doesn't, i mean, it's a dipole that means the positive and negative charges will have the same magnitude just oppositing sign.

01:16 Therefore, the electric force that they both experience will be of the same magnitude just in opposite directions.

01:23 Now, if we look at the 45 degree angle, and i'm just gonna keep this direction of the electric field as is, instead of drawing it every single time, and i am just going to draw the dipole in the orientation presented.

01:39 So in this case, the same rule still applies.

01:43 The positive charge still experiences an electric force that is in the direction of the electric field.

01:50 So it will experience a rightward force, and this will be leftward force.

01:57 Now, in the previous question, these two forces cancel out.

02:02 And notice how because these two forces are, they don't have any perpendicular component relative to the lever arm.

02:14 So if this is the axis of rotation for the dipole and the distance between this point and the point of application of the force, this is called the lever arm.

02:24 If there is no perpendicular component between the force and the lever arm, then there is no torque applied, right? so there is not going to be torque for the first diagram.

02:38 No net torque.

02:39 Whereas here, notice, if this is your lever arm and this is your force, then there does exist a perpendicular component between the two.

02:50 So, for example, if you were to extend this lever arm dotted line right here and you can draw the perpendicular component of the force relative to that lever arm.

02:59 So there is indeed going to be a torque...

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