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A parallel plate capacitor with plate area $A$ and plate separation $d =2 \,m$ has a capacitance of $4 \,\mu F$. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant $K =3$ (as shown in figure) will be .........$ \mu \,F$
The adjacent diagram shows a charge $+Q$ held on an insulating support $S$ and enclosed by a hollow spherical conductor. $O$ represents the centre of the spherical conductor. and $P$ is a point such that $OP = x $ and $SP = r$ . The electric field at point $P$ will be
The area of each plate of a parallel plate capacitor is $20\,cm^2$ and separation between the plates is $2\,mm$. If dielectric strength of air is $3 \times 10^6\,V/m,$ the maximum possible value of emf of the battery, which can be connected across the plates of this capacitor and the corresponding charge on the plates is
The capacitance of a parallel plate capacitor is $C$ when the region between the plate has air. This region is now filled with a dielectric slab of dielectric constant $k$. The capacitor is connected to a cell of $emf$ $E$, and the slab is taken out
Assertion : Charges are given to plates of two plane parallel plate capacitors $C_1$ and $C_2$ (such that $C_2 = 2C_1$ ) as shown in figure. Then the key $K$ is pressed to complete the circuit. Finally the net charge on upper plate and net charge the circuit. Finally the net charge on upper plate and net charge on lower plate of capacitor $C_1$ is positive.
Reason : In a parallel plate capacitor both plates always carry equal and opposite charge.
Condenser $A$ has a capacity of $15\,\mu F$ when it is filled with a medium of dielectric constant $15$. Another condenser $B$ has a capacity of $1\,\mu F$ with air between the plates. Both are charged separately by a battery of $100\;V$. After charging, both are connected in parallel without the battery and the dielectric medium being removed. The common potential now is.....$V$
Two charged particles of masses $m$ and $2m$ have charges $+2q$ and $+q$ respectively. They are kept in uniform electric field and allowed to move for some time. The ratio of their kinetic energies will be