An infinitely long thin wire, having a uniform charge density per unit length of $5 nC / m$, is passing through a spherical shell of radius $1 m$, as shown in the figure. A $10 nC$ charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points $P$ and $R$, in Volt, is. . . .

[Given: In SI units $\frac{1}{4 \pi \in_0}=9 \times 10^9, \ln 2=0.7$. Ignore the area pierced by the wire.]

  • A$110$
  • B$115$
  • C$170$
  • D$171$
IIT 2024, Medium
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
    $100$ capacitors each having a capacity of $10\,\mu F$ are connected in parallel and are charged by a potential difference of $100\,kV$. The energy stored in the capacitors and the cost of charging them, if electrical energy costs $108\;paise\;per\;kWh$, will be
    View Solution
  • 2
    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-
    View Solution
  • 3
    The metal plate on the left in figure carries a charge $+q$. The metal plate on the right has a charge of $-2q$. What charge will flow through $S$ when it is closed, if central plate is initially neutral
    View Solution
  • 4
    The radius of nucleus of silver (atomic number $=$ $47$) is $3.4 \times {10^{ - 14}}\,m$. The electric potential on the surface of nucleus is $(e = 1.6 \times {10^{ - 19}}\,C)$
    View Solution
  • 5
    Three identical capacitors (initial charge zero) are connected in series combination and charged through a battery of emf $E$ . After removing battery two resistances are connected to these capacitors as given. The heat dissipated in each of the resistance is
    View Solution
  • 6
    Two concentric hollow conducting spheres of radius $r$ and $R$ are shown. The charge on outer shell is $Q$. What charge should be given to inner sphere so that the potential at any point $P$ outside the outer sphere is zero?
    View Solution
  • 7
    What is the area of the plates of a $3\,F$ parallel plate capacitor, if the separation between the plates is $5\,mm$
    View Solution
  • 8
    The distance between the plates of a parallel plate capacitor is $d$. A metal plate of thickness $d/2$ is placed between the plates. The capacitance would then be
    View Solution
  • 9
    Three concentric metal shells $A, B$ and $C$ of respective radii $a, b$ and $c (a < b < c)$ have surface charge densities $+\sigma,-\sigma$ and $+\sigma$ respectively. The potential of shell $B$ is
    View Solution
  • 10
    If initial charge on all the capacitors were zero, work done by the battery in the circuit shown is ........... $mJ$
    View Solution