Two spherical conductors $A$ and $B$ of radius $a$ and $b (b > a)$ are placed in air concentrically $B$ is given charge $+ Q$ coulomb and $A$ is grounded. The equivalent capacitance of these is
A$4\pi {\varepsilon _0}\frac{{ab}}{{b - a}}$
B$4\pi {\varepsilon _0}\,(a + b)$
C$4\pi {\varepsilon _0}b$
D$4\pi {\varepsilon _0}\frac{{{b^2}}}{{b - a}}$
Medium
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D$4\pi {\varepsilon _0}\frac{{{b^2}}}{{b - a}}$
d (d)
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The capacitance of a parallel plate capacitor with air as medium is $6\, \mu F$. With the introduction of a dielectric medium, the capacitance becomes $30\, \mu F$. The permittivity of the medium is..........$C ^{2} N ^{-1} m ^{-2}$
$\left(\varepsilon_{0}=8.85 \times 10^{-12} C ^{2} N ^{-1} m ^{-2}\right)$
After the switch shown in figure $A$ is closed, there is current $i$ through resistance $R$. Figure $B$ indicates current variation curves $a, b, c$ and $d$ for four sets of values of $R$ and capacitance $C$:
$(i)$ $R_0$ and $C_0$, $(ii)$ $2R_0$ and $C_0$,
$(iii)$ $R_0$ and $2C_0$, $(iv)$ $2R_0$ and $2C_0$.
Which set goes with which curve?
A capacitor with capacitance $5\,\mu F$ is charged to $5\,\mu C.$ If the plates are pulled apart to reduce the capacitance to $2\,\mu F,$ how much work is done?
Two positrons $(e^+)$ and two protons $(p)$ are kept on four corners of a square of side $a$ as shown in figure. The mass of proton is much larger than the mass of positron. Let $q$ denotes the charge on the proton as well as the positron then the kinetic energies of one of the positrons and one of the protons respectively after a very long time will be-