*65. mmh An empty capacitor has a capacitance of 3.2 µF and is connected to a 12-V battery. A dielectric material (k = 4.5) is inserted between the plates of this capacitor. What is the magnitude of the surface charge on the dielectric that is adjacent to either plate of the capacitor?

(Hint: The surface charge is equal to the difference in the charge on the plates with and without the dielectric.)

As before we know the relationships for a capacitor with and without a dielectric are:

Without dielectric

And with a dielectric

Now since the battery is connected the voltage is constant. So we have

Since the capacitance changes with a dielectric by

Solving for

So with a dielectric

And without a dielectric

And with a dielectric

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