# What is the difference between direction of magnetic field and sense of magnetic field?

In my textbook, it has been given that if we apply Maxwell's Right hand grip rule, to a current carrying conductor(grip the conductor with the right hand) then we get the direction of the magnetic field by the curl of the fingers of our right hand. But i think that is not the direction since it should be along straight lines and not along circles(curls) and should be the direction of the force acting on the particle at a point. So what does the curl of the fingers indicate actually?

• Can't answer be simply : Both are same. Or heading must be edited. – Anubhav Goel Nov 7 '16 at 17:09

The magnetic field is not pointing in the same direction as the magnetic force it causes. In fact, it is always perpendicular.

Look at the formula:

$$\vec F=q \vec v \times \vec B$$

A cross product will always give a perpendicular result. The righthand rule with curling fingers gives you the field $\vec B$ direction, but you must then use the other right hand rule (with three fingers stretched) to find the force $\vec F$ direction.

You are maybe confusing it with electric fields and forces? They are related as:

$$\vec F=q\vec E$$

and are thus always parallel. But keep those two topics separated.

Furthermore, as the other answers show, field lines are in general not necessarily straight lines. Only in special cases. And that counts for all types of fields.

• How does the curl of the fingers give the direction of the magnetic field?I don't understand how can direction be curved? – MrAP Nov 7 '16 at 17:10
• @MrAP Direction is simply changing at every small time dt – Anubhav Goel Nov 7 '16 at 17:13
• @AnubhavGoel, do you mean to say that the curve indicates all the possible changed directions? – MrAP Nov 7 '16 at 17:15
• Curve indicates that at every small interval dt direction of field is changing by $d\theta$ angle in a particular direction. – Anubhav Goel Nov 7 '16 at 17:22
• @MrAP A line can be curved. Try to google electric field lines, and you'll see plenty examples. On each point on such curved line, you can point in the direction, it goes. And magnetic field lines happen to run around the current carrying wire. Because of that your fingers curl around the wire just as the field lines do. – Steeven Nov 7 '16 at 18:13

First off, magnetic field lines (of any general conductor) need not be straight lines. All of them form closed loops.

Here, I think you are talking about a long straight conductor. Upon using Maxwell's laws (laws that tell us how magnetic field is for any conductor), we get that they form circles. An easy way of remembering them is the Right hand Grip rule.

But i think that is not the direction since it should be along straight lines and not along circles(curls) and should be the direction of the force acting on the particle at a point.

Why not? The magnetic field does circulate around the wire following "circles". This is the result of the direct application of the Lorentz force law, which tells you that the force $\vec{F}$ and the field $\vec{B}$ must be perpendicular. See if this image helps:

Also, see this explanation from Hyperphysics and this related question, which might be what you're looking for.

The answer to your question is: curl of the fingers indicate the direction of magnetic field.You are partially correct to say that direction should always be 'straight' but the statement is incomplete.The curling action produces an imaginary circle around the current carrying conductor and at every point of the 'circle' we draw a tangent to find the direction of the field at that point of space (and tangent is one of the 'straightest thing' I guess). As stated above in other answers clearly the force on a particle in a magnetic field depends on its velocity hence your statement regarding the direction of force is incomplete as it is.