A solid conducting sphere, having a charge $Q$, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be $V$. If the shell is now given a charge of $-4\, Q$, the new potential difference between the same two surface is......$V$
JEE MAIN 2019, Diffcult
Download our app for free and get started
As given in the first condition:
Both conducting spheres are shown.
${V_{in}} - {V_{{\text{out }}}} = \left( {\frac{{{\text{kQ}}}}{{{r_1}}}} \right) - \left( {\frac{{{\text{kQ}}}}{{{{\text{r}}_2}}}} \right)$
$ = {\text{kQ}}\left( {\frac{1}{{{{\text{r}}_1}}} - \frac{1}{{{{\text{r}}_2}}}} \right) = V$
In the second condition:
Shell is now given charge $-4 Q$
${V_{in}} - {V_{out}} = \left( {\frac{{kQ}}{{{r_1}}} - \frac{{4kQ}}{{{r_2}}}} \right) - \left( {\frac{{kQ}}{{{r_2}}} - \frac{{4kQ}}{{{r_2}}}} \right)$
$ = \frac{{kQ}}{{{r_1}}} - \frac{{kQ}}{{{r_2}}}$
$=\mathrm{kQ}\left(\frac{1}{\mathrm{r}_{1}}-\frac{1}{\mathrm{r}_{2}}\right)=\mathrm{V}$
Hence, we also obtain that potential difference does not depend on charge of outer sphere.
$\therefore $ $P.d.$ remains same.
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
- 1Three condensers each of capacitance $2F$ are put in series. The resultant capacitance is.........$F$View Solution
- 2A hollow metal sphere of radius $5\,\, cm$ is charged so that the potential on its surface is $10\,\, V$. The potential at the centre of the sphere is.....$V$View Solution
- 3The diagram shows three capacitors with their capacitances and with breakdown voltages. What should be the maximum value of external $emf$ of source such that no capacitor breaks downView Solution
- 4$2\,\mu F$ capacitance has potential difference across its two terminals $200\;volts$. It is disconnected with battery and then another uncharged capacitance is connected in parallel to it, then $P.D.$ becomes $20\;volts$. Then the capacity of another capacitance will be.......$\mu F$View Solution
- 5In 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?
- 6An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in figure.If it is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the surface carries a uniform charge density $ '\sigma '$View Solution
If the charge $q_A$ is slowly moved inside the shell, then choose the statement$(s)$
- 7$A B C$ is a right angled triangle situated in a uniform electric field $\vec{E}$ which is in the plane of the triangle. The points $A$ and $B$ are at the same potential of $15 \,V$ while the point $C$ is at a potential of $20 \,V . A B=3 \,cm$ and $B C=4 \,cm$. The magnitude of electric field is (in $S.I.$ Units)View Solution
- 8If $4 \times {10^{20}}eV$ energy is required to move a charge of $0.25$ coulomb between two points. Then what will be the potential difference between them......$V$View Solution
- 9A $10\, micro-farad$ capacitor is charged to $500\, V$ and then its plates are joined together through a resistance of $10\, ohm$. The heat produced in the resistance is........$J$View Solution
- 10In an isolated parallel plate capacitor of capacitance $C$, the four surface have charges ${Q_1}$, ${Q_2}$, ${Q_3}$ and ${Q_4}$ as shown. The potential difference between the plates isView Solution
