The diagram shows the field lines around the Moon. Is the field uniform or radial?
Earlier lessons drew Earth's field two different ways. One picture showed arrows pointing in toward the whole planet from every side. Another showed straight parallel arrows pointing down into a room. They cannot both be right. Can they?
This lesson explains why a field that is really radial can honestly be drawn uniform near the surface.
Here are the two pictures side by side: the whole-Earth view, and a room-sized patch of the same field.
In the whole-Earth view, the field is radial: every line points in toward Earth's center.
Now zoom in on a patch the size of a room, or even a whole building. A building is tiny compared with Earth's radius of about 6,400 kilometers.
Across that tiny patch, the inward-pointing lines aim in almost exactly the same direction: straight down. Their spreading is just as small: over a few meters, the lines stay evenly spaced.
Parallel, evenly spaced lines are exactly the picture of a uniform field.
A diagram covers one classroom near Earth's surface. Which way is Earth's field drawn there?
The numbers back this up. From street level to the top of the tallest skyscraper, g changes by less than 0.1%.
Both pictures are right. Radial describes the whole field; uniform describes any region tiny compared with the planet's radius.
Why can a field that is really radial be drawn uniform across a classroom?
A crane lifts a beam 100 meters up a construction site. Should the engineers treat g as changed at the top?
100 meters is tiny compared with Earth's radius of about 6,400 km.
Over that region, the field's lines are effectively parallel and evenly spaced.
No. They treat the field as uniform: g is 9.8 N/kg at the ground and at the top.
A mission chart shows Earth's field out to five Earth radii. May the chartmaker draw parallel, evenly spaced lines?
Five Earth radii is not tiny compared with Earth's radius.
Across that region the lines visibly spread apart and change direction.
No. At that scale the field must be drawn radial.
Lena says Earth's field is really radial even where a lab diagram draws it uniform. Is she correct?
An elevator climbs from street level to a skyscraper's top floor, 800 meters up. How does g at the top compare with g at the street?
A mission chart spans the space from Earth's surface out to five Earth radii. How must Earth's field be drawn there?
Astronauts map the Moon's field across their landing site, a few hundred meters wide. Why may they draw it uniform?