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We apply force to insert a dielectric slowly between capacitor .

While inserting , we are assuming charge is constant.

Now my sir told that

Work done by external agent $= Q^2 /2C[(1/k)-1].$

I could not why it is negative as according to me this should be the work done by force to insert it. And the direction slab displaces and force is same , so it should be positive m

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The dielectric will feel an attractive force as you start to insert it in between the plates of the capacitor (because of polarization). Thus, the field is doing work on the force holding back the dielectric - conversely, that force is doing negative work.

When all is done, the energy stored in the capacitor with the dielectric is less than it was for the capacitor with the air gap. The difference is the work that was done BY the capacitor ON the dielectric.

From this, the signs should follow.

Note that the voltage will change (since capacitance is increasing and the charge is constant).

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  • $\begingroup$ So what is external agent $\endgroup$ – Icandoahandstand99 Feb 5 '17 at 20:17
  • $\begingroup$ Not sure what you mean by your question. "something" is holding the dielectric and slowly inserting it (resisting the force that is pulling it in). That is the "external agent". $\endgroup$ – Floris Feb 5 '17 at 20:18

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