A parallel plate capacitor with a dielectric | vedclass

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(A) Let the area of the plates be $A$, the distance between them be $d$, and the dielectric constant be $k$. The capacitor can be modeled as two capac

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(A) Let the area of the plates be $A$, the distance between them be $d$, and the dielectric constant be $k$. The capacitor can be modeled as two capacitors in parallel: one with the dielectric and one without.If the slab is pulled out at a constant speed $v$, the length of the slab inside the capacitor at time $t$ is $l' = l - vt$, where $l$ is the initial length of the slab.The capacitance $C$ at time $t$ is given by:$C(t) = \frac{\epsilon_0 (A - lw) + \epsilon_0 k (lw)}{d}$, where $w$ is the width of the plate.Since the slab is pulled out, the area occupied by the dielectric decreases linearly with time: $A_{dielectric} = w(l - vt)$.Thus, $C(t) = \frac{\epsilon_0}{d} [ (A - wl) + k \cdot w(l - vt) ]$.This simplifies to $C(t) = C_0 - \frac{\epsilon_0 w k v}{d} t$.Since $C(t)$ is a linear function of time with a negative slope, the capacitance decreases linearly as the slab is pulled out. Therefore, the graph is a straight line with a negative slope.

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