A charge is spread non-uniformly on the surface of a hollow sphere of radius $R$, such that the charge density is given by $\sigma=\sigma_0(1-\sin \theta)$, where $\theta$ is the usual polar angle. The potential at the centre of the sphere is
KVPY 2009, Medium
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
- 1View SolutionA long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.
- 2View SolutionThe figure shows a diagonal symmetric arrangement of capacitors and a battery.Identify the correct statements.
- 3Two capacitors ${C_1} = 2\,\mu \,F$ and ${C_2}\, = \,6\,\mu \,F$ in series, are connected in parallel to a third capacitor ${C_3} = \,4\,\mu \,F$. This arrangement is then connected to a battery of $e.m.f.$ $=$ $2V$, as shown in the figure. How much energy is lost by the battery in charging the capacitorsView Solution
- 4In the circuit shown in figure $C_1=2C_2$. Switch $S$ is closed at time $t=0$. Let $i_1$ and $i_2$ be the currents flowing through $C_1$ and $C_2$ at any time $t$, then the ratio $i_1/ i_2$View Solution
- 5At 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?View Solution
[take $\ln 5=1.6, \ln 3=1.1]$
- 6Two opposite and equal charges $4 \times {10^{ - 8}}\,coulomb$ when placed $2 \times {10^{ - 2}}\,cm$ away, form a dipole. If this dipole is placed in an external electric field $4 \times {10^8}\,newton/coulomb$, the value of maximum torque and the work done in rotating it through $180^\circ $ will beView Solution
- 7Two circuits $(a)$ and $(b)$ have charged capacitors of capacitance $C, 2C$ and $3C$ with open switches. Charges on each of the capacitor are as shown in the figures. On closing the switchesView Solution
- 8A point dipole $\vec p = - {p_0}\hat x$ is kept at the origin. The potential and electric field due to this dipole on the $y-$ axis at a distance $d$ are, respectively : (Take $V = 0$ at infinity)View Solution
- 9$27$ similar drops of mercury are maintained at $10 \,V$ each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ....... times that of a smaller drop.View Solution
- 10Effective capacitance between $A$ and $B$ in the figure shown is (all capacitance are in $\mu F$)View Solution
