JEE Mains · Physics · STD 12 - Electric potential and capacitance
- JEE Mains 2019
- Hard
- MCQ
A charge \(Q\) is distributed over three concentric spherical shell of radii \(a, b, c (a < b < c)\) such that their surface charge densities are equal to one another. The total potential at a point at distance \(r\) from their common centre, where \(r < a\), would be
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(\frac{{Q\,\left( {a + b + c} \right)}}{{4\pi \,{ \in _0}\,\left( {{a^2} + {b^2} + {c^2}} \right)\,\,}}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{Q}_{1}+\mathrm{q}_{2}+\mathrm{Q}_{3}=\mathrm{Q}.........(1)\)
\(\frac{\mathrm{Q}_{1}}{4 \pi \mathrm{a}^{2}}=\frac{\mathrm{Q}_{2}}{4 \pi \mathrm{b}^{2}}=\frac{\mathrm{Q}_{3}}{4 \pi \mathrm{c}^{2}}=\mathrm{k}.........(2)\)
Subs. \(Q_{1}, Q_{2}, Q_{3}\) in \(( 1)\)
\(k=\frac{Q}{4 \pi\left(a^{2}+b^{2}+c^{2}\right)}\)
\(v=\frac{k Q_{1}}{a}+\frac{k Q_{2}}{b}+\frac{k Q_{3}}{c}\)
More questions from Physics
- A force is applied to a steel wire ' \(A\) ', rigidly clamped at one end. As a result elongation in the wire is \(0.2\,mm\). If same force is applied to another steel wire ' \(B\) ' of double the length and a diameter \(2.4\) times that of the wire ' \(A\) ', the elongation in the wire ' \(B\) ' will be \(............\times 10^{-2}\,mm\) (wires having uniform circular cross sections)JEE Mains 2023 Medium
- As shown in figure, a cuboid lies in a region with electric field \(E=2 x^2 \hat{i}-4 y \hat{j}+6 \hat{k} \quad N / C\). The magnitude of charge within the cuboid is \(n \varepsilon_0 C\). The value of \(n\) is \(............\) (if dimension of cuboid is \(1 \times 2 \times 3 \;m ^3\) )
JEE Mains 2023 Medium - Surface tension of a soap bubble is \(2.0 \times 10^{-2}\; Nm ^{-1}\). Work done to increase the radius of soap bubble from \(3.5\; cm\) to \(7\; cm\) will be \(.........\times 10^{-4}\,J\) [Take \(\pi=\frac{22}{7}\) ]JEE Mains 2023 Medium
- In photoelectric effect an em-wave is incident on a metal surface and electrons are ejected from the surface. If the work function of the metal is 2.14 eV and stopping potential is 2 V , what is the wavelength of the em-wave ?
(Given hc \(=1242 \mathrm{eVnm}\) where h is the Planck's constant and c is the speed of light in vaccum.)JEE Mains 2025 Easy - Match List\(-I\) with List\(-II.\)
Choose the correct answer from the options given belowList\(-I\) List\(-II\) \((a)\) Capacitance, \(C\) \((i)\) \({M}^{1} {L}^{1} {T}^{-3} {A}^{-1}\) \((b)\) Permittivity of free space, \(\varepsilon_{0}\) \((ii)\) \({M}^{-1} {L}^{-3} {T}^{4} {A}^{2}\) \((c)\) Permeability of free space, \(\mu_{0}\) \((iii)\) \({M}^{-1} L^{-2} T^{4} A^{2}\) \((d)\) Electric field, \(E\) \((iv)\) \({M}^{1} {L}^{1} {T}^{-2} {A}^{-2}\) JEE Mains 2021 Medium - A metal block of base area \(0.20\,m ^2\) is placed on a table, as shown in figure. A liquid film of thickness \(0.25\,mm\) is inserted between the block and the table. The block is pushed by a horizontal force of \(0.1\,N\) and moves with a constant speed. If the viscosity of the liquid is \(5.0 \times 10^{-3} \;Pa-s\), the speed of block is \(.........\times 10^{-3}\,m / s\)
JEE Mains 2023 Medium