JEE Mains · Physics · STD 12 - Electric potential and capacitance
- JEE Mains 2024
- Hard
- Numerical
The distance between charges \(+\mathrm{q}\) and \(-\mathrm{q}\) is \(2 l\) and between \(+2 \mathrm{q}\) and \(-2 \mathrm{q}\) is \(4 l\). The electrostatic potential at point \(P\) at a distance \(r\) from centre \(O\) is \(-\alpha\left[\frac{q l}{r^2}\right] \times 10^9 \mathrm{~V}\), where the value of \(\alpha\) is _______. (Use \(\left.\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-2}\right)\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(27\)
Step-by-step Solution
Detailed explanation
\(\mathrm{V}=\frac{\mathrm{K} \dot{\mathrm{p}} \cdot \overrightarrow{\mathrm{r}}}{\mathrm{r}^3}=\frac{9 \times 10^9(6 \mathrm{q} \ell)}{\mathrm{r}^2} \cos \left(120^{\circ}\right)\)
\(=-(27)\left(\frac{\mathrm{q} \ell}{\mathrm{r}^2}\right) \times 10^9 \mathrm{Nm}^2 \mathrm{c}^{-2}\)
\(\Rightarrow \alpha=27\)
More questions from Physics
- If microwaves, \(X\) rays, infrared, gamma rays, ultraviolet, radio waves and visible parts of the electromagnetic spectrum by are denoted \(M, X, I, G, U, R\) and \(V\) then which of the following is the arrangement in ascending order of wavelength ?JEE Mains 2014 Easy
- In the figure shown, a circuit contains two identical resistors with resistance \(R = 5\,\Omega \) and an inductance with \(L = 2\, mH\). An ideal battery of \(15\, V\) is connected in the circuit. What will be the current through the battery long after the switch is closed?......\(A\)
JEE Mains 2019 Medium - Five persons \(P_1, P_2, P_3, P_4\) and \(P_5\) recorded object distance (u) and image distance (v) using same convex lens having power +5 D as \((25,96),(30,62)\), \((35,37),(45,35)\) and \((50,32)\) respectively. Identify correct statementJEE Mains 2026 Hard
- A block of mass \(1 \,kg\) attached to a spring is made to oscillate with an initial amplitude of \(12\, cm\). After \(2\, minutes\) the amplitude decreases to \(6\, cm\). Determine the value of the damping constant for this motion. (take In \(2=0.693\) )JEE Mains 2021 Hard
- The pressure acting on a submarine is \(3 \times 10^{5}\;Pa\) at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be: (Assume that atmospheric pressure is \(1 \times 10^{5} \;Pa\) density of water is \(10^{3}\, kg \,m ^{-3}, g =10 \,ms ^{-2}\) )JEE Mains 2021 Medium
- A polyatomic ideal gas has \(24\) vibrational modes. What is the value of \(\gamma\) ?JEE Mains 2021 Hard
More PYQs from JEE Mains
- A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is \(y \pi \times 10^{-2} \mathrm{~s}\), where the value of \(y\) is ________.
(Acceleration due to gravity, \(g=10 \mathrm{~m} / \mathrm{s}^2\), density of water \(=10^3 \mathrm{~kg} / \mathrm{m}^3\) )JEE Mains 2025 Hard - An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ______ \(\times 10^{-1} \mathrm{~J}\).
(Take \(\pi=3.14\))
JEE Mains 2025 Medium - A force \(\mathrm{F}=\alpha+\beta \mathrm{x}^2\) acts on an object in the x -direction. The work done by the force is 5 J when the object is displaced by 1 m . If the constant \(\alpha=1 \mathrm{~N}\) then \(\beta\) will be ________.JEE Mains 2025 Easy
- A particle of charge \(q\) and mass \(m\) is moving with a velocity \(-v \hat{ i }(v \neq 0)\) towards a large screen placed in the \(Y - Z\) plane at a distance \(d.\) If there is a magnetic field \(\overrightarrow{ B }= B _{0} \hat{ k },\) the minimum value of \(v\) for which the particle will not hit the screen isJEE Mains 2020 Medium
- Binding energy of a certain nucleus is \(18 \times 10^8 J\). How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus?JEE Mains 2024 Medium