A vacuum-insulated parallel-plate capacitor with plate separation has capacitance . What is the capacitance if an insulator with dielectric constant and thickness is slipped between the electrodes without changing the plate separation?
If an insulator with dielectric constant and thickness is slipped between the electrodes without changing the plate separation then the capacitance is
Parallel-plate capacitor with plate separation
If we insert an insulator into such a capacitor with separation and , then we can treat it as two capacitors connected in series, each with thickness and
It is clear that the capacitance of the air half will be
Since the capacitance is given as
The capacitance of the other half will then clearly be
Resulting capacitance of the considered system will be
The resulting capacitance will be
Hence, the capacitance is
Two 5.0 mm * 5.0 mm electrodes are held 0.10 mm apart and are attached to a 9.0 V battery. Without disconnecting the battery, a 0.10-mm-thick sheet of Mylar is inserted between the electrodes. What are the capacitor’s potential difference, electric field, and charge
(a) before and
(b) after the Mylar is inserted?
An ideal parallel-plate capacitor has a uniform electric field between the plates, zero-field outside. By superposition, half the field strength is due to one plate and a half due to the other.
a. The plates of a parallel-plate capacitor are oppositely charged and attract each other. Find an expression in terms of and the plate separation for the force one plate exerts on the other.
b. What is the attractive force on each plate of a capacitor with a plate spacing when charged to ?
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