# Recent questions and answers in Electrostatic Potential and Capacitance

### If one of the two electrons of a $H_2$ molecule is removed, we get a hydrogen molecular ion$find potential energy of system. ### Two charged conducting spheres of radii a and b are connected to each other by a wire. What is the ratio of electric fields at the surfaces of the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions. ### In a hydrogen atom, the electron and proton are bound at a distance of about$0.53 \dot{A}$: What is the minimum work required to free the electron, given that its kinetic energy in the orbit is half the magnitude of potential energy obtained ? ### In a hydrogen atom, the electron and proton are bound at a distance of about 0.53 Å: Estimate the potential energy of the system in eV, taking the zero of the potential energy at infinite separation of the electron from proton. ### A spherical conducting shell of inner radius$r_1$and outer radius$r_2$has a charge Q. Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain. ### Determine the electrostatic potential energy of a system consisting of two charges$7 \mu C$and$–2 \mu C$(and with no external field) placed at$(–9 cm, 0, 0)$and$(9 cm, 0, 0)$respectively.mple 2.5 (a) Determine the electrostatic potential energy of a system consisting of two charges 7 µC and –2 µC (and with no external field) placed at (–9 cm, 0, 0) and (9 cm, 0, 0) respectively.Suppose that the same system of charges is now placed in an external electric field$E = A (1/r^2); A = 9 \times 10^5 C m^{–2}$. What would the electrostatic energy of the configuration be? ### Determine the electrostatic potential energy of a system consisting of two charges$7 \mu C$and$–2\;\mu C$(and with no external field) placed at$(–9 cm, 0, 0)$and$(9 cm, 0, 0)$respectively. ### A$4 \mu F$capacitor is charged by a$200\; V$supply. It is then disconnected from the supply, and is connected to another uncharged$2 \mu F$capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation? ### A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of$2.5 \mu C$. The space between the concentric spheres is filled with a liquid of dielectric constant$32$. What is the potential of the inner sphere? ### A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of$2.5 \mu C$. The space between the concentric spheres is filled with a liquid of dielectric constant$32$. Determine the capacitance of the capacitor. ### A cylindrical capacitor has two co-axial cylinders of length$15\; cm$and radii$1.5\; cm$and$1.4\; cm$. The outer cylinder is earthed and the inner cylinder is given a charge of$3.5\; \mu C\$. Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effects (i.e., bending of field lines at the ends).

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