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The plates of an air capacitor are 3.0 mm apart…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The plates of an air capacitor are mm apart. We want to raise its capacitance by the factor with a slab that does not touch the plates. How thick must a slab of dielectric constant be? How thick must a metal slab be?
Need a reminder? The key ideaShow
A dielectric that fills the gap multiplies by . With the battery connected stays and grows by . With the battery removed stays and falls to . A slab of thickness gives , and the field in the slab is of the field in the air. A metal slab gives .
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. . A capacitance times larger needs an effective gap of mm.
Step 1. The dielectric slab. mm. So , and mm.
Step 2. The metal slab. mm, so mm.
Answer: mm of dielectric, or mm of metal.
Check. With mm the effective gap is . It fits.
What if? A metal slab does more for the same thickness, since it has . This is why a thinner metal slab does the job.
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