This subsubtopic is about identifying direction, not size. At any chosen point in space, the magnetic field from a moving charge is set by the geometry of the charge’s motion and the point’s location.

Core idea

A moving charge creates a magnetic field around itself, but that field does not point directly away from the charge and does not point along the charge’s motion. Instead, the field direction at a selected point depends on two vectors already present in the situation:

• the charge’s velocity

• the position vector from the charge to the point where the field is being found

The magnetic field vector at that point must be perpendicular to both of these vectors. This means the direction of the field is determined by a three-dimensional relationship. In many diagrams, both the velocity and the position vector are drawn in the plane of the page, so the magnetic field often points into or out of the page.

This perpendicular rule is the essential idea for this subsubtopic. If a proposed magnetic field direction lies partly along the charge’s path or partly along the line connecting the charge to the observation point, it cannot be correct.

Building the direction from two vectors

To find the magnetic field direction at a point, imagine freezing the motion at one instant and then constructing the geometry.

• First, identify the direction the charge is moving.

• Next, draw the position vector from the charge to the observation point.

• Then, determine the direction that is at right angles to both of those vectors.

Because there are two opposite directions that are perpendicular to the same plane, the sign of the charge matters. A positive charge gives one of those directions, while a negative charge gives the opposite direction.

This is why a positive charge and a negative charge moving in the same direction do not create magnetic fields pointing the same way at a given point. The location may be unchanged, and the motion may be unchanged, but reversing the sign of the source charge reverses the field direction.

A helpful geometric picture is that the magnetic field wraps around the line of motion of the charge.

Magnetic field lines form concentric circles around a straight “line source” (here, a current-carrying wire), illustrating the idea that the field direction is tangential rather than radial. The dot/cross symbols indicate current coming out of or going into the page, and the arrows show how the circulation direction reverses accordingly. Source

At points surrounding that line, the field vectors are tangent to a circular pattern. The important point here is not the size of the field, but the fact that the direction is always sideways relative to the motion.

Notice that moving the observation point changes the direction of the field even when the charge keeps moving in the same way. That happens because the position vector changes, so the required perpendicular direction changes as well.

Using the right-hand rule

The standard tool for choosing the correct perpendicular direction is the right-hand rule for a positive charge.

• Point the fingers of your right hand in the direction of the charge’s velocity.

• Curl your fingers toward the position vector drawn from the charge to the observation point.

• Your thumb gives the direction of the magnetic field.

For a negative charge, reverse the direction you found with the right hand.

Right-hand-rule illustration showing how the direction outcome changes when the moving charge is positive versus negative. The diagram emphasizes that the same geometric setup can yield opposite directions once the source charge’s sign is accounted for, which is essential when interpreting into/out-of-page results in 2D drawings. Source

This method works because it captures the required perpendicular relationship in a consistent way. It also helps distinguish between the two opposite directions that are both mathematically perpendicular to the same plane.

When applying this rule, the order matters. You must use the charge’s velocity first and the position vector second. If you reverse those vectors, you reverse the direction you predict. That is a common source of error in diagram-based questions.

On many diagrams, it helps to redraw the velocity vector and the position vector so they begin at the same location. That makes the plane containing the two vectors easier to see and makes the final perpendicular direction easier to identify.

Another useful check is to ask whether the final field direction is truly perpendicular to both arrows you started with. If it is not, then the right-hand rule was applied incorrectly or the position vector was drawn in the wrong direction.

Interpreting the field in space

This topic is easier when you remember that the field direction is local. You are not finding one single direction for the entire space around the charge. Instead, you determine the direction separately at each chosen point.

Two points can be the same distance from the moving charge but still have different magnetic field directions. What matters is the direction of each point’s position vector relative to the charge’s velocity.

You can think of the velocity, the position vector, and the magnetic field as forming a mutually perpendicular set in the simplest cases. That is why the answer is often not one of the obvious left-right or up-down directions already visible in the sketch.

In a flat diagram, this three-dimensional idea can be hidden. A correct answer may be represented with common symbols:

• a dot means out of the page

• a cross means into the page

These symbols are often the natural result of the perpendicular rule, especially when both given vectors lie in the page.

Common mistakes to avoid

One mistake is confusing the magnetic field from a moving charge with the electric field from a point charge. The magnetic field is not radial. It does not simply point away from a positive charge or toward a negative charge.

Another mistake is drawing the position vector backward. The relevant vector goes from the charge to the point in space. If you draw it from the point back to the charge, your predicted field direction will be reversed.

Students also sometimes treat “perpendicular” as if any right-angle direction is acceptable. That is not enough. The direction must be perpendicular to both vectors, and the sign of the source charge must also be accounted for.

Finally, remember that this is a direction rule for the magnetic field created by the moving source charge itself. The input vector is the source charge’s velocity, not the motion of some other object that might later enter the field. Keeping that distinction clear helps prevent mixing up separate ideas in magnetism.