A parallel plate capacitor of plate area a and plate separation d is charged to potential difference V and then the battery is disconnected. A slab of dielectric costant K is then inserted between the plates of the capacitor so as to fill the space between the plates. If Q,E,and W denote, respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted) and work done on the system, in question, in the process of inserting the slab, then

Options

A. `Q=(epsilon_(0)AV)/(d)`
B. `Q=(epsilon_(0)KAV)/(d)`
C. `E=V//Kd`
D. `W=(epsilon_(0)AV^(2))/(2d)[1-1//K]`

Answer

A, C, D

Explanation

Battery ids removed .Therefore ,charge store in the plates will remain constant
`Q=CV=(epsilon_0A)/dv` or Q= constant
Now, dielectric stab is inserted. Therefore, C will increase.New capacity will be
`C'=KC=(epsilon_0KA)/d implies V'=Q/C'=V/K` and new electric field `E=(V')/(d)=v/(K-d)`
Potential energy stored in capacitor,
Initially `U_i=1/2CV^(2)=(epsilon_0AV^(2))/(2d)` , Finally,`U _f=1/2C'V^(2)=1/2((Kepsilon_0A)/(d))(V/K)^(2)=(epsilon_0AV^(2))/(2Kd)` Work done the system will be `| Delta |=(^(epsilon)0AV^(2))/(2d)(1-1/K) therefore` Correct option (A),(C) and (D).