A positive point charge $q$ is placed at a distance $2 R$ from the surface of a metallic shell of radius $R$. The electric field at centre of shell due to induced charge has magnitude
  • A
    Zero
  • B$\frac{1}{4 \pi \varepsilon_0} \frac{q}{9 R^2}$
  • C$\frac{1}{4 \pi \varepsilon_0} \frac{q}{4 R^2}$
  • D$\frac{1}{4 \pi \varepsilon_0} \frac{q}{R^2}$
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
    A parallel plate condenser is connected with the terminals of a battery. The distance between the plates is $6\,mm$. If a glass plate (dielectric constant $K = 9$) of $4.5\,mm$ is introduced between them, then the capacity will become.......$times$
    View Solution
  • 2
    Two capacitors $A$ and $B$ are connected in series with a battery as shown in the figure. When the switch $S$ is closed and the two capacitors get charged fully, then
    View Solution
  • 3
    Four identical thin, square metal sheets, $S_1, S_2, S_3$, and $S_4$, each of side $a$ are kept parallel to each other with equal distance $d( < < a)$ between them, as shown in the figure. Let $C_0=\varepsilon_0 a^2 / d$, where $\varepsilon_0$ is the permittivity of free space.

    Match the quantities mentioned in $List-I$ with their values in $List-II$ and choose the correct option.

    $List-I$ $List-II$
    ($P$) The capacitance between $S_1$ and $S_4$, with $S_2$ and $S_3$ not connected, is ($1$) $3 C_0$
    ($Q$) The capacitance between $S_1$ and $S_4$, with $S_2$ shorted to $S_3$, is ($2$) $C_0 / 2$
    ($R$) The capacitance between $S_1$ and $S_3$, with $S_2$ shorted to $S_4$, is ($3$) $C_0 / 3$
    ($S$) The capacitance between $S_1$ and $S_2$, with $S_3$ shorted to $S_1$, and $S_2$ shorted to $S_4$, is ($4$) $2 C_0 / 3$
      ($5$) $2 C_0$

    View Solution
  • 4
    Two identical parallel plate capacitors are connected in series to a battery of $100\,V$. A dielectric slab of dielectric constant $4.0$ is inserted between the plates of second capacitor. The potential difference across the capacitors will now be respectively
    View Solution
  • 5
    A parallel plate capacitor is of area $6\, cm^2$ and a separation $3\, mm$. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants $K_1 = 10, K_2 = 12$ and $K_3 = 14$. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be
    View Solution
  • 6
    A bullet of mass $m$ and charge $q$ is fired towards a solid uniformly charged sphere of radius $R$ and total charge $+ q$. If it strikes the surface of sphere with speed $u$, find the minimum speed $u$ so that it can penetrate through the sphere. (Neglect all resistance forces or friction acting on bullet except electrostatic forces)
    View Solution
  • 7
    Find the equivalent capacitance between $A$ and $B$.......$\mu f$
    View Solution
  • 8
    The mean free path of electrons in a metal is $4 \times 10^{-8} \;m$. The electric field which can give on an average $2 \;eV$ energy to an electron in the metal will be in units of $V / m$
    View Solution
  • 9
    A thin conducting spherical shell (center at $O$ ) having charge $Q_0$ , radius $R$ and three point charges $Q_0$ , $-2Q_0$ , $3Q_0$ are also kept at point $A$ , $B$ and $C$ respectively as shown. Find the potential at any point on the conducting shell. (Potential at infinity is assumed to be zero)
    View Solution
  • 10
    In the circuit shown, find $C$ if the effective capacitance of the whole circuit is to be $0.5\,\mu F.$ All values in the circuit are in $\mu F.$
    View Solution