Problem 8. (4 points) A partially filled capacitor. A capacitor is constructed f
ID: 1655099 • Letter: P
Question
Problem 8. (4 points) A partially filled capacitor. A capacitor is constructed from two square,
metallic plates of sides l and separation d. Charges +Q and -Q are placed on the plates, and the
power supply is then removed. A material of dielectric constant k = 3 is inserted a distance x into the capacitor
as shown in Fig. 7. Assume d is much smaller than x. If the equivalent capacitance of the partially filled
capacitor is two times bigger than the capacitancewithout dielectrics, what is the distance x?
Explanation / Answer
it can be treated like two parallel capacitors, charges on each will be Qx/L and Q - Qx/L
net capacitance = 2C = 2Q/V
2Q/V = 3Qx/LV + (Q-Qx/L)/V
2 = 3 x/L + 1 -x/L
1 = 2x/L
x = L/2
A is correct