Displacement Vector

Q. A parallel-plate capacitor is located horizontally so that one of its plates is submerged into a liquid while the other is over its surface. The permittivity of the liquid is equal to $ϵ$. Its density is equal to $\rho$. To what height will the level of the liquid in the capacitor rise after its plate get a charge of surface density $\sigma$ ?

1. No change in liquid level
2. $\frac{{\rho }^2({\in }^2-1)}{{\in }_0\rho g}$
3. $\frac{{\rho }^2({\in }^2-1)}{2{\in }_0\rho g{\in }^2}$
4. $\frac{{\rho }^2(\in -1)}{{\in }_0\rho g}$

Q. A parallel-plate capacitor is located horizontally so that one of its plates is submerged into a liquid while the other is over its surface. The permittivity of the liquid is equal to $ϵ$. Its density is equal to $\rho$. To what height will the level of the liquid in the capacitor rise after its plate get a charge of surface density $\sigma$ ?

1. No change in liquid level
2. $\frac{{\rho }^2({\in }^2-1)}{{\in }_0\rho g}$
3. $\frac{{\rho }^2({\in }^2-1)}{2{\in }_0\rho g{\in }^2}$
4. $\frac{{\rho }^2(\in -1)}{{\in }_0\rho g}$

Q. Two capacitors of capacitance C each are connected in series. If one of them is filled with dielectric substance (k = 6) and other is filled with dielectric substance (k = 3). The effective capacitance of the combination will be

समान धारिता C के दो संधारित्रों को श्रेणी में संयोजित किया जाता है। यदि इनमें से किसी एक संधारित्र को परावैद्यतु पदार्थ (k = 6) द्वारा भरा जाता है तथा अन्य संधारित्र को परावैद्यतु पदार्थ (k = 3) द्वारा भरा जाता है। तब संयोजन की प्रभावी धारिता होगी

1. $\frac{C}{2}$
2. 2C
3. $\frac{C}{3}$
4. 8C