Magnetic Field - Dot and Cross Notation

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We visualized the nature of the magnetic field around the current carrying conductor with the help of right hand thumb rule.

Magnetic field is three dimensional in nature. To represent it in two dimensions, dot and cross notation is used.

Let us understand dots and crosses with the help of a model.

We will cut this toothpick and make it as an arrow. This is the arrowhead and this is the rear side marked by cross.

Let us take this cardsheet. It represents a horizontal plane.

Wire, our current carrying conductor is placed on this plane.

If an arrow is coming out of the paper, it will look like a dot from the top.

If an arrow is going inside the paper, it will look like a cross from the top.

In our model, we will take a thick plastic sheet instead of paper.

We will call this our plane of reference in which wire is present.

Direction of current is from left to right.

Field entering the plane can be represented by an arrow like this.

Field coming out of the plane is represented by an arrow like this.

If we look at it from the top, for an arrow coming out of the plane, it looks like a dot.

For an arrow going into the plane, we see only a cross.

This is how fields are represented in two dimensions.

Here the direction of current is from your left to right side that is from positive terminal to negative terminal. This is represented by the right hand thumb. Direction of the magnetic field will be anticlockwise as per the curled fingers. This can be represented in a plane with the help of arrows. Arrow nearer to you is going inside the paper while an arrow away from you is coming out of the paper.

Arrow coming out of the paper can be represented as a dot while an arrow going inside the paper can be represented as a cross.

Now let us reverse the direction of current.

Direction of current is from your right side to left side, which is represented by the thumb as well.
The direction of the magnetic field is in clockwise direction as shown by the curled fingers.

Arrow nearer to you is coming out of paper and an arrow away from you is going inside the paper.

These can be represented by dots and crosses like this.

Hope this model will be helpful in understanding dot and cross notation.

Do try this at home.

#271_EM_MagneticFieldDotCrossNotation

Thank You.