A point charge of +4.0 nC is placed on a line through the centre of a sphere of radius 0.30 m…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A point charge of nC is placed on a line through the centre of a sphere of radius m. It is a distance from the centre. Find the net flux through the sphere when m and when m. Also find for comparison.
Need a reminder? The key ideaShow
Gauss's law: the net flux through a closed surface is , with . Only the net charge inside counts. The shape and size of the surface do not matter. For a sphere of radius with the charge at its centre, .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Decide for each position whether the charge is inside the sphere. Then use Gauss's law.
Step 1. The comparison number. .
Step 2. m. This is less than the radius m, so the charge is inside. The net flux is , wherever the charge sits inside.
Step 3. m. The charge is outside. Every line that enters the sphere leaves again, so the net flux is .
Answer: , and .
Check. The program adds over the sphere, ring by ring. It gives for every distance up to m and beyond m. The flux jumps as the charge crosses the surface.
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