JEE Mains · Physics · STD 12 - 2. Electric potential and capacitance
There are three co-centric conducting spherical shells \(A , B\) and C of radii \(a , b\) and c respectively. The potential of the spheres \(A , B\) and C respectively, are :
- A \(\frac{1}{4 \pi \epsilon_0}\left(\frac{q_1+q_2+q_3}{a}\right), \frac{1}{4 \pi \epsilon_0}\left(\frac{q_1+q_2+q_3}{b}\right), \frac{1}{4 \pi \epsilon_0}\left(\frac{q_1+q_2+q_3}{c}\right)\)
- B \(\frac{1}{4 \pi \epsilon_0}\left(\frac{q_1+q_2+q_3}{a}\right), \frac{1}{4 \pi \epsilon_0}\left(\frac{q_1+q_2}{b}+\frac{q_3}{c}\right), \frac{1}{4 \pi \epsilon_0}\left(\frac{q_1}{a}+\frac{q_2}{b}+\frac{q_3}{c}\right)\)
- C \(\frac{1}{4 \pi \epsilon_0}\left(\frac{q_1}{a}+\frac{q_2}{b}+\frac{q_3}{c}\right), \frac{1}{4 \pi \epsilon_0}\left(\frac{q_1+q_2}{b}+\frac{q_3}{c}\right), \frac{1}{4 \pi \epsilon_0}\left(\frac{q_1+q_2+q_3}{c}\right)\)
- D \(\frac{1}{4 \pi \epsilon_0}\left(\frac{q_1}{a}+\frac{q_2}{b}+\frac{q_3}{c}\right), \frac{1}{4 \pi \epsilon_0}\left(\frac{q_1+q_2+q_3}{b}\right), \frac{1}{4 \pi \epsilon_0}\left(\frac{q_1+q_2+q_3}{c}\right)\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{4 \pi \epsilon_0}\left(\frac{q_1}{a}+\frac{q_2}{b}+\frac{q_3}{c}\right), \frac{1}{4 \pi \epsilon_0}\left(\frac{q_1+q_2}{b}+\frac{q_3}{c}\right), \frac{1}{4 \pi \epsilon_0}\left(\frac{q_1+q_2+q_3}{c}\right)\)
Step-by-step Solution
Detailed explanation
\(V _{ A }=\frac{ Kq _1}{ a }+\frac{ Kq _2}{b}+\frac{ Kq _3}{ c }=\frac{1}{4 \pi \varepsilon_0}\left(\frac{ q _1}{ a }+\frac{ q _2}{b}+\frac{ q _3}{ c }\right)\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A capacitor of capacitance \(500\,\mu F\) is charged completely using a dc supply of \(100\,V\). It is now connected to an inductor of inductance \(50\,mH\) to form an \(LC\) circuit. The maximum current in \(LC\) circuit will be \(.........A\).JEE Mains 2022 Medium
- In \(Li^{++},\) electron in first Bohr orbit is excited to a level by a radiation of wavelength \(\lambda .\) When the ion gets deexcited to the ground state in all possible ways(including intermediate emission) a total of six spectral lines are observed. What is the value of \(\lambda \)?.....\(nm\) (Given: \(h = 6.63\times 10^{34}\,js; e = 3 \times 10^8\,ms^{-1}\) )JEE Mains 2019 Hard
- Half lives of two radioactive nuclei \(A\) and \(B\) are \(10\, minutes\) and \(20\, minutes\), respectively. If, initially a sample has equal number of nuclei, then after \(60\) \(minutes\) , the ratio of decayed numbers of nuclei \(A\) and \(B\) will beJEE Mains 2019 Hard
- In Young's double slit experiment the two slits are \(0.6 \; mm\) distance apart. Interference pattern is observed on a screen at a distance \(80 \; cm\) from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be \(\dots \; nm .\)JEE Mains 2022 Medium
- A Carnot engine with efficiency \(50\,\%\) takes heat from a source at \(600\,K\). In order to increase the efficiency to \(70\,\%\), keeping the temperature of sink same, the new temperature of the source will be \(.........\,K\)JEE Mains 2023 Medium
- The density and breaking stress of a wire are \(6 \times\) \(10^4 \mathrm{~kg} / \mathrm{m}^3\) and \(1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2\) respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is \(\frac{1^{\text {rd }}}{3}\) of the value on the surface of earth. The maximum length of the wire with breaking is _______ \(\mathrm{m}\) (take, \(\mathrm{g}=\) \(\left.10 \mathrm{~m} / \mathrm{s}^2\right)\)JEE Mains 2024 Hard
More PYQs from JEE Mains
- Given below are two statements : Statement \((I)\) : dimensions of specific heat is \(\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]\) Statement \((II)\) : dimensions of gas constant is \(\left[\mathrm{ML}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}\right]\)JEE Mains 2024 Hard
- What will be the most suitable combination of three resistors \(A =2\, \Omega, B =4\, \Omega, C =6\, \Omega\) so that \(\left(\frac{22}{3}\right)\Omega\) is equivalent resistance of combination\(?\)JEE Mains 2022 Medium
- The de-Broglie wavelength \(({\lambda _B})\) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state \(({\lambda _G})\) byJEE Mains 2018 Medium
- To know the resistance \(G\) of a galvanometer by half deflection method, a battery of \(emf\, V_E\) and resistance \(R\) is used to deflect the galvanometer by angle \(\theta \). If a shunt of resistance \(S\) is needed to get half deflection then \(G, R\) and \(S\) related by the equationJEE Mains 2016 Hard
- For \(\mathrm{a}, \mathrm{b}>0\), let \(f(x)=\left\{\begin{array}{l}\frac{\tan ((a+1) x)+b \tan x}{x}, x<0 \\ \frac{\sqrt{a x+b^2 x^2}-\sqrt{a x}}{b \sqrt{a} x \sqrt{x}}, x>0\end{array}\right.\) be a continous function at \(x=0\). Then \(\frac{b}{a}\) is equal toJEE Mains 2024 Hard
- Among the statements:
(S1) : If A(5, -1) and B(-2, 3) are two vertices of a triangle, whose orthocentre is (0, 0), then its third vertex is (-4, -7) and
(S2) : If positive numbers 2a, b, c are three consecutive terms of an A.P., then the lines ax + by + c = 0 are concurrent at (2, -2)JEE Mains 2026 Medium