- #1
amaresh92
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greetings,
why the radii of the tip of lightning rod is small(few mm)?
thanks.
why the radii of the tip of lightning rod is small(few mm)?
thanks.
In summary, the conversation revolves around the question of why the radii of the tip of a lightning rod are small (a few mm). It is explained that the electric field is greater where the radius of curvature is smaller, and in equilibrium, there must be a higher charge density at a decreasing radius. The exact dependency on curvature is unknown. Another topic discussed is the field at the surface of a conducting sphere, where it is mentioned that the field depends on the radius of the sphere.
- #2
tiny-tim
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hiamaresh92! 
put a lightning rod near a flat metal plate …
what will happen if you place a charge near them?
put a lightning rod near a flat metal plate …
what will happen if you place a charge near them?
- #3
Meir Achuz
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The electric field is greater where the radius of curvature of the end is smaller.
- #4
tiny-tim
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Meir Achuz said:
because at a point of increasing radius of curvature, if two charges on opposite sides are at equal distances measured along the surface, the one on the side of smaller radius of curvature will be actually nearer …
so in equilibrium, …
ooh, that's the wrong result, isn't it?
ah … let's start again
…at radius of curvature r, the amount of charge in an arc between fixed distances s and s + ds (measured in 3D space, not along the surface) will be less for greater r (by a factor cos(s/r), the radius of the arc), and its component along the surface will also be less (by a factor cos(s/2r)) …
so for smaller r, s/r is larger and so cos(s/r) and cos(s/2r) are smaller, and so the amount of charge and its "component" (loosely speaking) at a fixed distance is smaller, so the repulsive force will be smaller on the side of decreasing r
so in equilibrium, there must be a higher charge density at decreasing r!
(does anyone know the exact dependency on curvature?)
- #5
Meir Achuz
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A simple case is a conducting sphere of radius R with a charge Q.
How does the field at the surface depend on R?
How does the field at the surface depend on R?
- #6
tiny-tim
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Meir Achuz said:
??
R is constant.1. Why are lightning rod tip radii so small?
The size of lightning rod tip radii is determined by the principle of electric field reduction. The smaller the radius, the higher the electric field concentration, which is necessary to draw lightning strikes away from the protected structure.
2. Can lightning rod tip radii be larger for better protection?
No, increasing the size of the lightning rod tip radius may actually decrease its effectiveness. A larger radius would result in a lower electric field concentration, making the rod less effective in attracting lightning strikes.
3. Are there any safety concerns with small lightning rod tip radii?
While smaller lightning rod tip radii may seem less safe, they are actually designed to safely handle the high voltage of a lightning strike. The small radius allows for a more concentrated electric field, which helps to dissipate the strike's energy and prevent damage to the protected structure.
4. How do scientists determine the optimal size for lightning rod tip radii?
Scientists use mathematical calculations and simulations to determine the optimal size for lightning rod tip radii. These calculations take into account factors such as the height of the structure, the expected lightning strike frequency, and the electrical properties of the surrounding environment.
5. Are there any other factors besides size that affect the effectiveness of lightning rod tip radii?
Yes, the material and shape of the lightning rod also play a role in its effectiveness. A highly conductive material and a pointed shape can further enhance the rod's ability to attract lightning strikes. Proper installation and regular maintenance are also crucial for optimal protection.
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