Electrostatic Potential and Capacitance

The total charge on the system of capacitors $C_1=1\mu F,C_2=2\mu F,C_3=4\mu Fand{C}_4=3\mu F$ connected in parallel is:

(Assume a battery of 20V is connected to the combination)

A body having specific charge 8 $\mu C/g$  is resting on a frictionless plane a t a distance 10cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V/m is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be_________s.

A capacitor is connected to a 20 V battery through a resistance of 10 $\Omega .$ <!-- [if gte mso 9]><xml> </xml><![endif]--> It is found that the potential difference across the capacitor rises to 2V in 1 $\mu s.$ <!-- [if gte mso 9]><xml> </xml><![endif]--> The capacitance of the capacitor is________ <!-- [if gte mso 9]><xml> </xml><![endif]-->  $\mu F.$

Given  $In\left(\frac{10}{9}\right)=0.105$

A parallel plate capacitor of capacitance 200 $\mu F$ <!-- [if gte mso 9]><xml> </xml><![endif]--> is connected to a battery of 200V. A dielectric slab of dielectric constant 2 is now inserted into the space between plates of capacitor while the battery remain connected. The change in the electrostatic energy in the capacitor will be_______J.

Two particles A and B having charges 20 $\mu C$ <!-- [if gte mso 9]><xml> </xml><![endif]--> and $5\mu C$ - <!-- [if gte mso 9]><xml> </xml><![endif]-->respectively are held fixed with a separation of 5cm. At what position a third charged particle should be placed so that it does not experience a net electric force?

Calculate the amount of charge on capacitor of 4 $\mu F.$ <!-- [if gte mso 9]><xml> </xml><![endif]--> The internal resistance of battery is <!-- [if gte mso 9]><xml> </xml><![endif]-->  $1\Omega$

A parallel-plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant K₁ and K₂ of same area A/2 and thickness d/2 are inserted in the space between the plates. The capacitance of the capacitor will be given by:

 

The two thin coaxial rings, each of radius ‘a’ and having charges +Q and -Q respectively are separated by a distance of ‘s’. The potential difference between the centres of the two rings is:

The material filled between the plates of a parallel plate capacitor has resistivity 200 <!-- [if gte mso 9]><xml> </xml><![endif]--> The value of capacitance of the capacitor is 2 pF. If a potential difference of 40V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is: (given the value of relative permittivity of material is 50)

A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius b as shown in figure. The approximate variation electric field $\overrightarrow{E}$ <!-- [if gte mso 9]><xml> </xml><![endif]--> as a function of distance r from centre O is given by: