When I searched the net about magnetic field lines, Wikipedia told something about contour lines and that magnetic materials placed along a magnetic field has some specific loci, which i did not understand. Can someone explain it to me in details. Also how do we know that tangent to a magnetic field line gives the direction of magnetic field? I am very confused.
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Both Electric & Magnetic lines of force are introduced as an aid of visualizing electric and magnetic fields. Magnetic lines of force are imaginary straight or curved paths along which a free (isolated) North pole would travel when placed in magnetic field. In case of electric field lines, the term unit positive charge is used. These concepts of field lines were introduced by Faraday and both of these fields are related by Maxwell equations. Both electric as well as magnetic field lines have similar properties... They're thought to flow but, no actual movement occurs. The direction of these lines is from North pole to South pole outside the magnet whereas in the inside, it's the other way around. And, They're always continuous closed loops extending throughout the magnetic source and never intersect each other. The crowding or sparsity of these field lines depend upon the intensity of the magnetic source... These field lines are best understood (why they're imagined..?) by a home-experiment which has been followed for years. Take a wire and cardboard. Throw some metal fillings over the board. Pass some current (somewhat higher for noticeable effect). Tap the board gently. The fillings would arrange themselves in the form of curves. And the direction of this field is given by Maxwell's right hand Cork Screw rule... Or just use a bar magnet instead of catching a live-wire. Why are tangents then..? Place a magnetic compass somewhere in a magnetic field (Say, a bar magnet like the one below). The needle would align tangentially to the magnetic lines of force. Still If you aren't able to swallow, please learn "What are tangents? then..!" |
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I think Crazy Buddy has covered most of it. But I'm just adding a couple of points that may (or may not) help your understanding of this - The magnetic field lines (or electric field, or any field lines for that matter) are defined such that the tangent to the field line at a point gives the direction of the field at that point. That's all there is to it, really. But since it is after all just a curve in space, it has to have an equation. A plot of these equations will help you visualize what the field lines look like. As this guy at Physics Forum has explained, the equation for a magnetic field line (in polar co-ordinates) in 2 dimensions is given by $$\frac{B_r}{B_\theta} = \frac{dr}{rd\theta}$$ where $B_r$ is the radial component of the magnetic field and $B_\theta$ is the angular component. So a plot of these equations will give you lines that look like the ones you see in textbooks and Wikipedia. Note: This is the field line equations only for a magnetic dipole (a regular magnet). If you have a more complicated magnetic system, these field equations will no longer hold. |
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