Two metallic spheres of radii $1\,\, cm$ and $3\,\, cm$ are given, charges of $-1$$ \times {10^{ - 2}}$ $C$ and $5$$ \times {10^{ - 2}}\,C$ respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is
AIPMT 2012, Medium
Download our app for free and get started
When the given metallic spheres are connected by a conducting wire, charge will flow till both the spheres acquire a common potential which is given by Common potential,
$V =\frac{q_{1}+q_{2}}{C_{1}+C_{2}}=\frac{-1 \times 10^{-2}+5 \times 10^{-2}}{4 \pi \varepsilon_{0} R_{1}+4 \pi \varepsilon_{0} R_{2}}$
$=\frac{4 \times 10^{-2}}{4 \pi \varepsilon_{0}\left(1 \times 10^{-2}+3 \times 10^{-2}\right)}$
$=\frac{4 \times 10^{-2}}{4 \pi \varepsilon_{0} \times 4 \times 10^{-2}}.........(i)$
$\therefore $ Final charge on the bigger sphere
$=4 \pi \varepsilon_{0} \times 3 \times 10^{-2} \times \frac{4 \times 10^{-2}}{4 \pi \varepsilon_{0} \times 4 \times 10^{-2}}(\mathrm{Using}(\mathrm{i}))$
$=3 \times 10^{-2} \mathrm\,{C}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionThe potential gradient is a
- 2If a charged spherical conductor of radius $10\,cm$ has potential $V$ at a point distant $5\,cm$ from its centre, then the potential at a point distant $15\,cm$ from the centre will beView Solution
- 3In the figure, the inner (shaded) region $A$ represents a sphere of radius $r_A=1$, within which the electrostatic charge density varies with the radial distance $r$ from the center as $\rho_A=k r$, where $k$ is positive. In the spherical shell $B$ of outer radius $r_B$, the electrostatic charge density varies as $\rho_{\bar{B}}=\frac{2 k}{r}$. Assume that dimensions are taken care of. All physical quantities are in their $SI$ units.View Solution
Which of the following statement($s$) is(are) correct?
- 4Combination of two identical capacitors, a resistor $R$ and a $DC$ voltage source of voltage $6\; V$ is used in an experiment on $C-R$ circuit. It is found that for a parallel combination of the capacitor the time in which the voltage of the fully charged combination reduces to half its original voltage is $10\; s$. For series combination the time needed for reducing the voltage of the fully charged series combination by half isView Solution
- 5Three long concentric conducting cylindrical shells have radii $R, 2R$ and $2\sqrt 2 $ $ R$ . Inner and outer shells are connected to each other. The capacitance across middle and inner shells per unit length is:View Solution
- 6Three infinitely long linear charges of charge density $\lambda $ , $\lambda $ and $-2\lambda $ are placed in space. A point in space is specified by its perpendicular distance $r_1 , r_2 $ and $ r_3$ respectively from the linear charges. For the points which are equipotentialView Solution
- 7Four capacitors are connected in a circuit as shown in the figure. The effective capacitance in $\mu F$ between points $A$ and $B$ will beView Solution
- 8A capacitor when filled with a dielectric $K = 3$ has charge ${Q_0}$, voltage ${V_0}$ and field ${E_0}$. If the dielectric is replaced with another one having $K = 9$ the new values of charge, voltage and field will be respectivelyView Solution
- 9A fully charged capacitor has a capacitance $‘C’$. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity $‘s’$ and mass $‘m’$. If the temperature of the block is raised by ‘$\Delta T$’, the potential difference $‘V’$ across the capacitance isView Solution
- 10Two capacitors of equal capacitance $(C_1 = C_2)$ are shown in the figure. Initially, while the switch $S$ is open, one of the capacitors is uncharged and the other carries charge $Q_0$. The energy stored in the charged capacitor is $U_0$. Sometimes after the switch is closed, the capacitors $C_1$ and $C_2$ carry charges $Q_1$ and $Q_2$, respectively; the voltages across the capacitors are $ V_1$ and $V_2$; and the energies stored in the capacitors are $U_1$ and $U_2$. Which of the following statements is INCORRECT ?View Solution
