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?
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Can't answer be simply : Both are same. Or heading must be edited. – Anubhav Goel Nov 07 '16 at 17:09
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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.
Steeven
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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 07 '16 at 17:10
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@AnubhavGoel, do you mean to say that the curve indicates all the possible changed directions? – MrAP Nov 07 '16 at 17:15
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Curve indicates that at every small interval dt direction of field is changing by $d\theta$ angle in a particular direction. – Anubhav Goel Nov 07 '16 at 17:22
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@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 07 '16 at 18:13
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@MrAP And no, a direction doesn't necessarily have to be straight. In this case we are talking about a direction clockwise or counterclockwise. And that is what your fingers show with the right hand rule – Steeven Nov 07 '16 at 18:21
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even simpler: "Ampere in his seminal study of electrodynamics in 1823, found that a plane of electrodynamic action could be identified at any point in the neighborhood of a closed current-bearing circuit. When a current element lies in this plane it experiences a force directed along the plane and perpendicular to the element, whatever the orientation of the latter. This plane was perpendicular to the conventional direction of the magnetic intensity. Ampere called it the ‘directive plane’ " . The magnetic field is a "plane quantity" (an anti-symmetrical tensor) and not a vector. – hyportnex Nov 07 '16 at 20:44
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see Roche:"Axial vectors, skew-symmetric tensors and the nature of the magnetic field" , Eur. J. Phys. 22 (2001) 193–203, where he also quotes Sommerfeld: "It may be justifiable on the grounds of economy of expression to replace skew symmetrical tensors by vectors in ordinary vector analysis, but in some ways it hides the essential feature; it gives rise to the well-known “swimming rules” in electrodynamics, which in no wise signify that there is a unique direction of twist in the space in which electrodynamic events occur; – hyportnex Nov 07 '16 at 20:48
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they become necessary only because the magnetic intensity of field is regarded as a vector, whereas it is, in reality, a skew-symmetric tensor (like the so-called vectorial product of two vectors). If we had been given one more space-dimension, this could never have occurred." – hyportnex Nov 07 '16 at 20:49
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@hyportnex Ahm, "even simpler" might be too big a claim. But inarguably more in depth – Steeven Nov 07 '16 at 23:39
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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.
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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.
Skawang
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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.
quarkonium
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