Final answer:
The permittivity of the dielectric sheet can be found using the capacitance formulas for a parallel-plate capacitor, with and without a dielectric, and relating the current pulse provided to the change in stored charge.
Step-by-step explanation:
To find the permittivity of the dielectric sheet, we use the relationship between capacitance, charge, voltage, and the dielectric properties of the material. The capacitance of a parallel-plate capacitor without a dielectric is given by C = ε0A/d, where ε0 is the permittivity of free space, A is the area of one plate, and d is the distance between the plates.
When a dielectric is inserted into the capacitor, the capacitance increases to C' = εrε0A/d, where εr is the relative permittivity (also known as the dielectric constant) of the dielectric material. The charge (Q) stored in a capacitor is given by Q = CV. In this case, we can find the charge before the dielectric is inserted because we have the voltage (V) and initially, the capacitor behaves like one without a dielectric (C = ε0A/d).
However, the question provides the current (I) during a pulse and the duration of the pulse (t). Since I = ΔQ/Δt, where ΔQ is the change in charge, we can calculate ΔQ = IΔt. This charge ΔQ comes from the change in capacitance by inserting the dielectric, which affects the voltage across the capacitor plates according to ΔQ = C'ΔV. We already know ΔQ from the current pulse information, so we can solve for εr by rearranging the equation C' = εrε0A/d and using the values of ΔQ, A, and d.