A circular disc of radius $R$ carries surface charge density $\sigma(r)=\sigma_{0}\left(1-\frac{r}{R}\right)$, where $\sigma_{0}$ is a constant and $r$ is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is $\phi_{0}$. Electric flux through another spherical surface of radius $\frac{R}{4}$ and concentric with the disc is $\phi$. Then the ratio $\frac{\phi_{0}}{\phi}$ is ______
Correct Answer: 6.4
Solution and Explanation
Then the ratio $\frac{\phi_{0}}{\phi}$ is \(\underline{6.40}.\)
Top Questions on electrostatic potential and capacitance
- Light consisting of two wavelengths 600 nm and 480 nm is used to obtain interference fringes in a double slit experiment. The screen is placed 1.0 m away from slits which are 1.0 mm apart. (i) Calculate the distance of the third bright fringe on the screen from the central maximum for wavelength 600 nm.
- CBSE CLASS XII - 2025
- Physics
- electrostatic potential and capacitance
- A ray of light is incident on a refracting face AB of a prism ABC at an angle of \( 45^\circ \). The ray emerges from face AC and the angle of deviation is \( 15^\circ \). The angle of prism is \( 30^\circ \). Show that the emergent ray is normal to the face AC from which it emerges out. Find the refraction index of the material of the prism.
- CBSE CLASS XII - 2025
- Physics
- electrostatic potential and capacitance
- A thin pencil of length \( f/4 \) is placed coinciding with the principal axis of a mirror of focal length \( f \). The image of the pencil is real and enlarged, just touches the pencil. Calculate the magnification produced by the mirror.
- CBSE CLASS XII - 2025
- Physics
- electrostatic potential and capacitance
- The electric field at a point in space is \( 2 \times 10^3 \, \text{N/C} \) and the potential at the same point is \( 100 \, \text{V} \). What is the potential energy of a charge of \( 5 \, \mu\text{C} \) placed at that point?
- MHT CET - 2025
- Physics
- electrostatic potential and capacitance
- Three infinitely long wires with linear charge density \( \lambda \) are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?
- JEE Main - 2025
- Physics
- electrostatic potential and capacitance
Questions Asked in JEE Advanced exam
The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting, movable piston of area $A$. The left and right compartments are filled with $\frac{3}{2}$ and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant $k$ and natural length $\frac{2L}{5}$. In thermodynamic equilibrium, the piston is at a distance $\frac{L}{2}$ from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is $P = \frac{kL}{A} \alpha$, then the value of $\alpha$ is ____
- JEE Advanced - 2025
- Thermodynamics
- The total number of real solutions of the equation $$ \theta = \tan^{-1}(2 \tan \theta) - \frac{1}{2} \sin^{-1} \left( \frac{6 \tan \theta}{9 + \tan^2 \theta} \right) $$ is
(Here, the inverse trigonometric functions $ \sin^{-1} x $ and $ \tan^{-1} x $ assume values in $[-\frac{\pi}{2}, \frac{\pi}{2}]$ and $(-\frac{\pi}{2}, \frac{\pi}{2})$, respectively.)- JEE Advanced - 2025
- Inverse Trigonometric Functions
- Let $$ \alpha = \frac{1}{\sin 60^\circ \sin 61^\circ} + \frac{1}{\sin 62^\circ \sin 63^\circ} + \cdots + \frac{1}{\sin 118^\circ \sin 119^\circ}. $$ Then the value of $$ \left( \frac{\csc 1^\circ}{\alpha} \right)^2 $$ is \rule{1cm}{0.15mm}.
- JEE Advanced - 2025
- Some Applications of Trigonometry
- One of the products formed from the reaction of permanganate ion with iodide ion in neutral aqueous medium is:
- JEE Advanced - 2025
- Redox reactions
Let $ S $ denote the locus of the point of intersection of the pair of lines $$ 4x - 3y = 12\alpha,\quad 4\alpha x + 3\alpha y = 12, $$ where $ \alpha $ varies over the set of non-zero real numbers. Let $ T $ be the tangent to $ S $ passing through the points $ (p, 0) $ and $ (0, q) $, $ q > 0 $, and parallel to the line $ 4x - \frac{3}{\sqrt{2}} y = 0 $.
Then the value of $ pq $ is- JEE Advanced - 2025
- Coordinate Geometry
Concepts Used:
Electrostatic Potential and Capacitance
Electrostatic Potential
The potential of a point is defined as the work done per unit charge that results in bringing a charge from infinity to a certain point.
Some major things that we should know about electric potential:
- They are denoted by V and are a scalar quantity.
- It is measured in volts.
Capacitance
The ability of a capacitor of holding the energy in form of an electric charge is defined as capacitance. Similarly, we can also say that capacitance is the storing ability of capacitors, and the unit in which they are measured is βfaradsβ.
Read More: Electrostatic Potential and Capacitance
The capacitor is in Series and in Parallel as defined below;
In Series
Both the Capacitors C1 and C2 can easily get connected in series. When the capacitors are connected in series then the total capacitance that is Ctotal is less than any one of the capacitorβs capacitance.
In Parallel
Both Capacitor C1 and C2 are connected in parallel. When the capacitors are connected parallelly then the total capacitance that is Ctotal is any one of the capacitorβs capacitance.