JEE Mains · Physics · STD 12 - Electric charges and fields
- JEE Mains 2022
- Medium
- MCQ
Two identical metallic spheres \(A\) and \(B\) when placed at certain distance in air repel each other with a force of \(F\). Another identical uncharged sphere \(C\) is first placed in contact with \(A\) and then in contact with \(B\) and finally placed at midpoint between spheres \(A\) and \(B\). The force experienced by sphere \(C\) will be.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(3\,F / 4\)
Step-by-step Solution
Detailed explanation
Let \(q _{ A }= q _{ B }= q\)
When \(C\) is placed in contact with \(A\), charge on \(A\) and \( C\) will be \(=\frac{ q }{2}\)
Now \(C\) is placed in contact with \(B\), charge on \(B\) and \(C\) will be \(=\frac{q+\frac{q}{2}}{2}=\frac{3 q}{4}\)
\(F ^{\prime}= F _{2}- F _{1}=\frac{\left( K \frac{3 q }{4}- K \frac{ q }{2}\right)}{\frac{ r ^{2}}{4}} \cdot \frac{3 q }{4}\)
\(=\frac{3 Kq ^{2}}{4 r ^{2}}=\frac{3 F }{4}\)
More questions from Physics
- Water drops are falling from a nozzle of a shower onto the floor, from a height of \(9.8\, {m}\). The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor. (In \(m\))JEE Mains 2021 Hard
- the given potentiometer has its wire of resistance \(10\, \Omega\). When the sliding contact is in the middle of the potentiometer wire, the potential drop across \(2\, \Omega\) resistor is -
JEE Mains 2021 Hard - Two narrow bores of diameter \(5.0\, {mm}\) and \(8.0\, {mm}\) are joined together to form a \(U-\)shaped tube open at both ends. If this \({U}\)-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water \({T}=7.3 \times 10^{-2} \, {Nm}^{-1}\), angle of contact \(=0, {g}=10\, {ms}^{-2}\) and density of water \(\left.=1.0 \times 10^{3} \,{kg} \,{m}^{-3}\right]\) (in \(mm\))JEE Mains 2021 Hard
- The energy density associated with electric field \(\overrightarrow{ E }\) and magnetic field \(B\) of an electromagnetic wave in free space is given by ( \(\epsilon_0-\) permittivity of free space, \(\mu_0\) - permeability of free space)JEE Mains 2023 Medium
- A charged particle going around in a circle can be considered to be a current loop. A particle of mass \(m\) carrying charge \(q\) is moving in a plane with speed \(v\) under the influence of magnetic field \(\overrightarrow{ B }\). The magnetic moment of this moving particleJEE Mains 2020 Hard
- A uniform solid cylinder of length \(L\) and radius \(R\) has moment of inertia about its axis equal to \(I_1\). A small co-centric cylinder of length \(L / 2\) and radius \(R / 3\) carved from this cylinder has moment of inertia about its axis equals to \(I_2\). The ratio \(I_1 / I_2\) is _________ .JEE Mains 2026 Hard
More PYQs from JEE Mains
- A closed organ pipe of length \(L\) and an open organ pipe contain gases of densities \(\rho_{1}\) and \(\rho_{2}\) respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is \(\frac{ x }{3} L \sqrt{\frac{\rho_{1}}{\rho_{2}}}\) where \(x\) is ......... . (Round off to the Nearest Integer)JEE Mains 2021 Easy
- A thin disc of mass \(M\) and radius \(R\) has mass per unit area \(\sigma (r) = kr^2\) where \(r\) is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane isJEE Mains 2019 Hard
- The typical transfer characteristic of a transistor in \(CE\) configuration is shown in figure. A load resistor of \(2\,k\Omega\) is connected in the collector branch of the circuit used. The input resistance of the transistor is \(0.50\,k \Omega\). The voltage gain of the transistor is.
JEE Mains 2022 Hard - A proton (mass \(m\) ) accelerated by a potential difference \(V\) flies through a uniform transverse magnetic field \(B.\) The field occupies a region of space by width \('d'\). If \(\alpha \) be the angle of deviation of proton from initial direction of motion (see figure), the value of \(sin\,\alpha \) will be
JEE Mains 2015 Hard - A part of a complete circuit is shown in the figure. At some instant, the value of current \(I\) is \(1\, A\) and it is decreasing at a rate of \(10^{2}\, A s ^{-1}\) The value of the potential difference \(V _{ P }- V _{ Q }\) (in volts) at that instant, is.
JEE Mains 2020 Medium - Distance of the centre of mass of a solid uniform cone from its vertex is \(z_0\) . If the radius of its base is \(R\) and its height is \(h\) then \(z_0\) is equal toJEE Mains 2015 Hard