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## Homework Statement

My teacher told me that the force will increase ##k^2## times, where ##k## is the dielectric constant, but I don't see how.

## Homework Equations

## The Attempt at a Solution

To start with, with no dielectric, the force between the plates is given by ##\frac{q^2}{2A\epsilon_{0}}##. If I do insert a dielectric, and The plates are connected to a battery, the charge becomes ##q'=kq##; as potential difference doesn't change (thanks to the battery) but capacitance does. So, when I replace ##q## by ##q'## in the above equation, I must also simultaneously change ##\epsilon_{0}## to ##k \epsilon_{0}##( as the medium has changed), so I get

##F'=\frac{k^2q^2}{2Ak\epsilon_{0}}=kF##, as one of the ##k##'s gets cancelled out. I am supposed to get ##k^2F##. What am I missing? Thanks in advance!!