A dielectric slab of thickness b is inserted between the plates of a parallel-plate capacitor of plate separation d. We have to show that the capacitance is given by

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Let the free charge on the parallel-plate capacitor be q. The electric field between the plates of the capacitor outside the dielectric is given by

and the electric field inside the dielectric slab is given by

Therefore, the potential difference between the plates will be

From the definition of capacitance

we note that