$A$ particle of charge $-q$ and mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear density $+\lambda$. Then the time period will be given as (Consider $k$ as Coulomb's constant).
- A$T^2=\frac{4 \pi^2 m}{2 k \lambda q} r^3$
- B$T=2 \pi r \sqrt{\frac{m}{2 k \lambda q}}$
- C$T=\frac{1}{2 \pi r} \sqrt{\frac{m}{2 k \lambda q}}$
- D$T=\frac{1}{2 \pi} \sqrt{\frac{2 k \lambda q}{m}}$
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Similar Questions
$A$ parallel plate capacitor consists of two metal plates. One plate is given a charge of $+q$,while the other is connected to the ground. Points $P, P_1$,and $P_2$ are taken as shown in the figure. At which point is the electric field $NOT$ zero?
Easy
View SolutionMatch List-$I$ with List-$II$:
List-$I$ List-$II$ $(A)$ Electric field inside (distance $r < R$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$ and radius $R$. $(I)$ $\sigma / \varepsilon_0$ $(B)$ Electric field at distance $r$ from a uniformly charged infinite plane sheet with surface charge density $\sigma$. $(II)$ $\sigma / 2 \varepsilon_0$ $(C)$ Electric field outside (distance $r > R$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$ and radius $R$. $(III)$ $0$ $(D)$ Electric field between $2$ oppositely charged infinite plane parallel sheets with uniform surface charge density $\sigma$. $(IV)$ $\frac{\sigma R^2}{\varepsilon_0 r^2}$
Choose the correct answer from the options given below:
| List-$I$ | List-$II$ |
| $(A)$ Electric field inside (distance $r < R$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$ and radius $R$. | $(I)$ $\sigma / \varepsilon_0$ |
| $(B)$ Electric field at distance $r$ from a uniformly charged infinite plane sheet with surface charge density $\sigma$. | $(II)$ $\sigma / 2 \varepsilon_0$ |
| $(C)$ Electric field outside (distance $r > R$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$ and radius $R$. | $(III)$ $0$ |
| $(D)$ Electric field between $2$ oppositely charged infinite plane parallel sheets with uniform surface charge density $\sigma$. | $(IV)$ $\frac{\sigma R^2}{\varepsilon_0 r^2}$ |
Choose the correct answer from the options given below:
If a small sphere of mass $m$ and charge $q$ is hung from a silk thread at an angle $\theta$ with the surface of a vertical charged conducting plate,then for equilibrium of the sphere,the surface charge density of the plate is
Medium
View SolutionWithin a spherical charge distribution of charge density $\rho(r)$,$N$ equipotential surfaces of potential $V_0, V_0 + \Delta V, V_0 + 2\Delta V, \dots, V_0 + N\Delta V$ (where $\Delta V > 0$) are drawn and have increasing radii $r_0, r_1, r_2, \dots, r_N$,respectively. If the difference in the radii of the surfaces is constant for all values of $V_0$ and $\Delta V$,then:
DifficultJEE MAIN 2016
View SolutionAn isolated sphere of radius $R$ contains a uniform volume distribution of positive charge. Which of the curves shown below correctly illustrates the dependence of the magnitude of the electric field of the sphere as a function of the distance $r$ from its centre?
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