The Deceptive Nature of Field Lines

[astro2cosmos]

what is the meaning of deceptivness of field line??
i mean for 2d surface field line = n/2pi*r (f.l. inversly proportional to r) but for 3d surface f.l.= n/4pi*r^2 (f.l. inversly proportional to r^2), since electric field = kq/r^2??
what is the reason behind it?

it written in the introduction to electrodynamics of griffin//////

 

[HallsofIvy]

what is the meaning of deceptivness of field line??
i mean for 2d surface field line = n/2pi*r (f.l. inversly proportional to r) but for 3d surface f.l.= n/4pi*r^2 (f.l. inversly proportional to r^2), since electric field = kq/r^2??
what is the reason behind it?

it written in the introduction to electrodynamics of griffin//////

"Deceptiveness"? I don't believe I've ever seen that word in reference to field lines! If you are asking about why the 2d case is inversely proportional to r while the three dimensional case is inversely proportional to r², it's because your field is indicating a "uniform" spread.

Back when I was in high school, my physics teacher showed us what he called a "butter gun". It was just a squirt gun with four rods coming out the barrel in a sort of cone. Supposedly you put butter in the squirt gun, a piece of toast in the rods, and squirted button on your toast! His real point was that the farther your toast was from the gun, the larger it had to be to fit in the rods- and since area is always proportional to a distance squared, if your toast was twice as far from the gun, it had four times the area. Since the same amount of butter was spread over four times the area, the thickness of the butter was 1/4 as much- "inversely proportional to r²".


Now imagine a two dimensional version of the same thing. Now instead of four rods, you have two, bounding, say, the top and bottom, and your "toast" is the line from top to bottom. It is easy to show now that if the "toast" is twice as far from the gun, its length is twice as large so the same amount of butter is spread over twice the distance and so the thickness is 1/2 as much- "inversely proportional to r".

 

[astro2cosmos]

"Deceptiveness"? I don't believe I've ever seen that word in reference to field lines! If you are asking about why the 2d case is inversely proportional to r while the three dimensional case is inversely proportional to r², it's because your field is indicating a "uniform" spread.

Back when I was in high school, my physics teacher showed us what he called a "butter gun". It was just a squirt gun with four rods coming out the barrel in a sort of cone. Supposedly you put butter in the squirt gun, a piece of toast in the rods, and squirted button on your toast! His real point was that the farther your toast was from the gun, the larger it had to be to fit in the rods- and since area is always proportional to a distance squared, if your toast was twice as far from the gun, it had four times the area. Since the same amount of butter was spread over four times the area, the thickness of the butter was 1/4 as much- "inversely proportional to r²".


Now imagine a two dimensional version of the same thing. Now instead of four rods, you have two, bounding, say, the top and bottom, and your "toast" is the line from top to bottom. It is easy to show now that if the "toast" is twice as far from the gun, its length is twice as large so the same amount of butter is spread over twice the distance and so the thickness is 1/2 as much- "inversely proportional to r".

i don't understand this example if you have any other simple example then please give!

 

[buffordboy23]

Griffiths was basically saying that in nature/reality the strength of the field lines are inversely proportional to r^2. He was pointing out that the diagram of the field lines shows only two dimensions, so according to his diagram, the field lines appear to be inversely proportional to r.

More simply, he wants the reader to understand that while his plot of the field lines is illustrative, it does not agree with nature. The diagram should have a third dimension, but this is hard to represent and so it was omitted.

Clear now?