Charge variation upon inserting a dielectric slab into a conductor

Физика Электромагнетизм
1

Doubt:
I am having problem in understanding the variation of charge on capacitor when a dielectric slab is inserted into it. Can anyone please provide me a detailed explanation of this phenomenon? The case I am concerned with has a battery connected to the capacitor and hence constant potential difference is maintained.

Problem:

Screenshot (2316)
Screenshot (2316)1163×822 66.1 KB

1 лайк
2

I have read standard textbooks like E&M by Purcell and Morin, Classical Electrodynamics by Griffiths etc. But none of them were able to provide me a satisfactory analysis. I am able to solve the problems related to this topic however, I still don’t feel like I have a proper and in-depth understanding of this topic.

1 лайк
3

I think the correct answer for this problem should be (A). Am I right?

2 лайка
4

For a parallel plate capacitor

C=\frac{\varepsilon\varepsilon_0 x}{d}+\frac{\varepsilon_0(l-x)}{d}=\frac{\varepsilon_0(\varepsilon-1)x}{d}+\frac{\varepsilon_0l}{d}

SInce the dielectric is inserted between plates with constant acceleration x=\frac{at^2}{2}, then q=CV=\frac{\varepsilon_0(\varepsilon-1)at^2}{2d}+\frac{\varepsilon_0l}{d} . As \varepsilon>\varepsilon_0 the plot of q(t) is a parabola, which is “directed upward” and the answer is C.

3 лайка
5

Thanks! I made a big mistake in my assumption.

1 лайк