Dipole. A dipole is located on a sheet of paper. (a) In the plane of that paper, carefully sketc

Dipole. A dipole is located on a sheet of paper. (a) In the...

Key Concepts

Electric Dipole

An electric dipole consists of two equal and opposite point charges separated by a finite distance, creating a system with no net charge but a distinct electric dipole moment. This dipole moment is a vector pointing from the negative charge to the positive charge, and it defines the strength and orientation of the dipole. Dipoles are fundamental in understanding polarization, interactions of molecules, and the behavior of systems in external electric fields.

Electric Field Lines

Electric field lines graphically represent both the direction and the relative magnitude of the electric field. They originate at positive charges and terminate at negative charges, demonstrating the path a positive test charge would follow. The density of these lines in a region indicates the strength of the field there, with closer lines signifying a stronger field. In a dipole, the pattern of these lines reflects the interaction of the two opposite charges.

Equipotential Surfaces

Equipotential surfaces are regions in space where the electric potential is constant. In a two-dimensional diagram, these appear as equipotential curves. For any given charge configuration, moving along an equipotential surface does not change the potential energy of a charge. Importantly, these surfaces or curves are always perpendicular to the electric field lines, a property that is widely used to infer the field distribution and understand the work done by electric forces.

Relationship Between Field Lines and Equipotential Curves

The relationship between electric field lines and equipotential curves is a key concept in electrostatics. Because the electric field is the gradient of the potential, the field lines always intersect equipotential surfaces at right angles. This perpendicularity provides a visual tool for understanding how electric forces act in space and is crucial for correctly sketching both the field lines and the equipotential curves for any charge configuration, including a dipole.

Transcript

00:01 This question asks us to sketch the electric field lines for a dipole.

00:03 So a dipole consists of a positive and negative charge, and the field lines go from the positive to the negative charges.

00:12 You would sort of derive this behavior just by finding the electric field at each point due to the, by superimposing the fields due to either charge.

00:26 And then it looks sort of like this.

00:31 So they kind of come out here.

00:34 Oh, this should be, these should be exactly the same.

00:38 But, you know, i guess i got a little crazy with this one.

00:45 So i guess i can add another one here.

00:49 And then i'll add some other ones, some bigger ones out here to make it a little more even.

00:57 So kind of something like that.

01:01 And then, of course, it's not zero in the middle.

01:03 In the middle, it's strong and it goes sort of like that.

01:12 And so we want to find the equipotential lines.

01:15 So equipotential lines are where the potential energy or the potential is the same.

01:23 So for drawing equipotential lines, when you draw, they're always going to be perpendicular to your e -field.

01:29 So that's kind of a first clue.

01:32 And then so let's try to think which two points are going to be.

01:38 Potential.

01:40 So i mean, i would say that like, so you want to kind of look at the density of lines and figure out where the density of lines remains the same.

01:56 So these are my field lines, by the way, in case that wasn't clear.

02:00 So these are the actual field lines.

02:06 Let me pause to think about the best way to draw this.

02:14 So let's think about.

02:15 First this line that goes through between these two points.

02:20 So the potential, and that that would be this line.

02:24 So i'm going to draw the equipotential lines in red.

02:28 So let's think about what the potential is all along this point.

02:31 And then as i'm drawing it, i'm kind of alluding to the idea that it's all the same.

02:35 So the potential would be calculated by doing kq over r for each charge.

02:40 And since they're equal and opposite charges, those terms would be equal and opposite.

02:44 And so they would cancel.