The identical metal plates with large surface areas are kept parallel to each other as shown in figure. The left most plate is given a charge $Q$ , the rightmost a charge $-2Q$ and the middle one remains neutral. Find the charge appearing on the outer surface of the rightmost plate
Medium
Download our app for free and get started
Consider the Gaussian surface where the induced charge is as shown in the figure
The net field at $\mathrm{P}$ due to the charges is zero,
i.e.,
$-2 Q+\frac{q}{2 A \varepsilon_{0}}(l e f t)+\frac{q}{2 A \varepsilon_{0}}(r i g h t)+q-\frac{q}{2 A \varepsilon_{0}}(r i g h t)=0$
$\Rightarrow-2 q+1-Q+q=0$
$\Rightarrow q=\frac{3}{2} Q$
Charge on the right side of the rightmost plate is
$-2 Q+Q=-2 Q+\frac{3}{2} Q=-\frac{Q}{2} c$
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
- 1Three capacitors $C_1,\,C_2$ and $C_3$ are connected as shown in the figure to a battery of $V\,volt$. If the capacitor $C_3$ breaks down electrically the change in total charge on the combination of capacitors isView Solution
- 2An electric dipole of moment $\vec p$ is lying along a uniform electric field $\vec E.$ The work done in rotating the dipole by $90^o $ isView Solution
- 3Three concentric metallic spherical shell $A, B$ and $C$ or radii $a, b$ and $c$ $(a < b < c)$ have surface charge densities $- \sigma , + \sigma ,$ and $- \sigma $ respectively. The potential of shell $A$ is :View Solution
- 4A uniformly charged thin spherical shell of radius $\mathrm{R}$ carries uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $\mathrm{F}$ (see figure). $\mathrm{F}$ is proportional toView Solution
- 5If ${q}_{{f}}$ is the free charge on the capacitor plates and ${q}_{{b}}$ is the bound charge on the dielectric slab of dielectric constant $k$ placed between the capacitor plates, then bound charge $q_{b}$ can be expressed asView Solution
- 6Two insulating plates are both uniformly charged in such a way that the potential difference between them is $V_2 - V_1 = 20\ V$. (i.e., plate $2$ is at a higher potential). The plates are separated by $d = 0.1\ m$ and can be treated as infinitely large. An electron is released from rest on the inner surface of plate $1. $ What is its speed when it hits plate $2?$View Solution
$(e = 1.6 \times 10^{-19}\ C, m_e= 9.11 \times 10^{-31}\ kg)$
- 7Two metal spheres of capacitance ${C_1}$ and ${C_2}$ carry some charges. They are put in contact and then separated. The final charges ${Q_1}$ and ${Q_2}$ on them will satisfyView Solution
- 8A parallel plate capacitor of capacitance $12.5 \mathrm{pF}$ is charged by a battery connected between its plates to potential difference of $12.0 \mathrm{~V}$. The battery is now disconnected and a dielectric slab $\left(\epsilon_{\mathrm{r}}=6\right)$ is inserted between the plates. The change in its potential energy after inserting the dielectric slab is_______.$\times 10^{-12} \mathrm{~J}$.View Solution
- 9Minimum number of capacitors of $2\,\mu F$ capacitance each required to obtain a capacitor of $5\,\mu F$ will beView Solution
- 10If potential of $A$ is $10\,V$, then potential of $B$ isView Solution
