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
- 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?
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In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of \( P_1 \) and \( P_2 \) are orthogonal to each other. The polarizer \( P_3 \) covers both the slits with its transmission axis at \( 45^\circ \) to those of \( P_1 \) and \( P_2 \). An unpolarized light of wavelength \( \lambda \) and intensity \( I_0 \) is incident on \( P_1 \) and \( P_2 \). The intensity at a point after \( P_3 \), where the path difference between the light waves from \( S_1 \) and \( S_2 \) is \( \frac{\lambda}{3} \), is:
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(B) Ultraviolet rays (\( \lambda_2 \))
(C) Infrared rays (\( \lambda_3 \))
(D) X-rays (\( \lambda_4 \))
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Questions Asked in JEE Advanced exam
A positive, singly ionized atom of mass number $ A_M $ is accelerated from rest by the voltage $ 192 \, \text{V} $. Thereafter, it enters a rectangular region of width $ w $ with magnetic field $ \vec{B}_0 = 0.1\hat{k} \, \text{T} $. The ion finally hits a detector at the distance $ x $ below its starting trajectory. Which of the following option(s) is(are) correct?
$ \text{(Given: Mass of neutron/proton = } \frac{5}{3} \times 10^{-27} \, \text{kg, charge of the electron = } 1.6 \times 10^{-19} \, \text{C).} $
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- A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass \( m \) and radius \( r \) and is in a uniform vertical magnetic field \( B_0 \). When a current \( I \) is passed through the loop, the loop turns about the line PQ by an angle \( \theta \). The angle \( \theta \) is given by:
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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.