Two isolated conducting spheres $S_{1}$ and $S_{2}$ of radius $\frac{2}{3} R$ and $\frac{1}{3} R$ have $12\, \mu C$ and $-3\, \mu C$ charges, respectively, and are at a large distance from each other. They are now onnected by a conducting wire. A long time after this is done the charges on $S_{1}$ and $S_{2}$ are respectively
JEE MAIN 2020, Diffcult
Download our app for free and get started
Now
$Q _{1}+ Q _{2}= Q _{1}+ Q _{2}^{\prime}=12 \mu C -3 \mu C =9 \mu C$
$\& V_1=V_{2} \Rightarrow \frac{K Q_{1}^{\prime}}{\frac{2 R}{3}}=\frac{K Q_{2}^{\prime}}{\frac{R}{3}}$
$Q _{1}^{\prime}=2 Q _{2}^{\prime} \Rightarrow 2 Q _{2}^{\prime}+ Q _{2}^{\prime}=9 \mu C$
$\Rightarrow Q _{2}^{\prime}=3 \mu C$
$\ \quad Q_{1}^{\prime}=6 \mu C$
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
- 1In the circuit shown, initially there is no charge on capacitors and keys $S _1$ and $S _2$ are open. The values of the capacitors are $C _1=10 \mu F , C _2=30 \mu F$ and $C _3= C _4=80 \mu F$.View Solution
Which of the statement($s$) is/are correct ?
$(1)$ The keys $S _1$ is kept closed for long time such that capacitors are fully charged. Now key $S _2$ is closed, at this time, the instantaneous current across $30 \Omega$ resistor (between points $P$ and $Q$ ) will be $0.2 A$
$(2)$ If key $S _1$ is kept closed for long time such that capacitors are fully charged, the voltage difference between points $P$ and $Q$ will be $10 V$.
$(3)$ At time $t =0$, the key $S _1$ is closed, the instantaneous current in the closed circuit will be $25 mA$.
$(4)$ If key $S _1$ is kept closed for long time such that capacitors are fully charged, the voltage across the capacitors $C _1$ will be $4 V$.
- 2The electric field in a region surrounding the origin is uniform and along the $x$ - axis. A small circle is drawn with the centre at the origin cutting the axes at points $A, B, C, D$ having co-ordinates $(a, 0), (0, a), (-a, 0), (0, -a)$; respectively as shown in figure then potential in minimum at the pointView Solution
- 3View SolutionEquipotential surfaces are shown in figure. Then the electric field strength will be
- 4A spherical drop of capacitance $1\,\,\mu F$ is broken into eight drops of equal radius. Then, the capacitance of each small drop is ......$\mu F$View Solution
- 5The electric potential at a point $(x,\;y)$ in the $x - y$ plane is given by $V = - kxy$. The field intensity at a distance $r$ from the origin varies asView Solution
- 6A 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 beView Solution
- 7In the given circuit, charge $Q_2$ on the $2\ μF$ capacitor changes as $C$ is varied from $1\ μF$ to $3\ μF$. $Q_2$ as a function of '$C$' is given properly by: (figures are drawn schematically and are not to scale)View Solution
- 8The circuit shown in the figure consists of a charged capacitor of capacity $3\, \mu F$ and a charge of $30\, \mu C$. At time $t =0,$ when the key is closed, the value of current flowing through the $5\, M \Omega$ resistor is $'x'$ $\mu-A$. The value of $'x'$ to the nearest integer is .........View Solution
- 9On moving a charge of $20$ coulombs by $2 \;cm , 2 \;J$ of work is done, then the potential difference between the points is (in $volt$)View Solution
- 10A uniform electric field having a magnitude ${E_0}$ and direction along the positive $X - $ axis exists. If the potential $V$ is zero at $x = 0$, then its value at $X = + x$ will beView Solution