Aspherical shell with an inner radius $'a'$ and an outer radius $'b' $ is made of conducting material. Apoint charge $+Q$ is placed at the centre of the spherical shell and a total charge $- q $ is placed on the shell.

Assume that the electrostatic potential is zero at an infinite distance from the spherical shell. The electrostatic potential at a distance $R$ $(a < R < b)$ from the centre of the shell is (where $K = $ $\frac{1}{{4\pi {\varepsilon _0}}}$)

Medium
Download our app for free and get startedPlay store
To. Make electric field indide metal charge on iner surface of shell must vbe equal to $-Q$

$V_{p}=\frac{K Q}{R}-\frac{K Q}{R}+\frac{K(Q-q)}{b}=\frac{K(Q-q)}{b}$

art

Download our app
and 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

  • 1
    Find the ratio of energy stored in $5\,\mu F$ and $4\,\mu F$ capacitor in the given circuit in steady state
    View Solution
  • 2
    At time $\mathrm{t}=0$, a battery of $10 \mathrm{~V}$ is connected across points $\mathrm{A}$ and $\mathrm{B}$ in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them becomes $4$ volt?

    [take $\ln 5=1.6, \ln 3=1.1]$

    View Solution
  • 3
    A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume in the figure. The electric field inside the emptied space is
    View Solution
  • 4
    In the circuit shown below $C_1=10 \,\mu F , C_2=C_3=20 \,\mu F$, and $C_4=40 \,\mu F$. If the charge on $C_1$ is $20 \,\mu C$ then potential difference between $X$ and $Y$ is ......... $V$
    View Solution
  • 5
    Combination 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 is
    View Solution
  • 6
    Two conducting hollow sphere of radius $R$ and $3R$ are found to have $Q$ charge on outer surface when both are connected with a long wire and $q'$ charge is kept at the centre of bigger sphere. Then which one is true
    View Solution
  • 7
    Two metal pieces having a potential difference of $800 \;V$ are $0.02\; m$ apart horizontally. A particle of mass $1.96 \times 10^{-15} \;kg$ is suspended in equilibrium between the plates. If $e$ is the elementary charge, then charge on the particle is
    View Solution
  • 8
    There is an air filled $1\,pF$ parallel plate capacitor. When the plate separation is doubled and the space is filled with wax, the capacitance increases to $2\,pF$. The dielectric constant of wax is
    View Solution
  • 9
    Two charged parallel plate capacitors, each with separation between plates equal to $d$, are separated by a large distance $L >> d$. Then the force of interaction between them is proportional to
    View Solution
  • 10
    If the capacitance of each capacitor in the tetrahedron shown is $C$ , then effective capacitance of the network across any two junctions is ......$C$
    View Solution