A simple pendulum of length $L$ is placed between the plates of a parallel plate capacitor having electric field $E,$ as shown in figure. Its bob has mass $m$ and charge $q.$ the time period of the pendulum is given by
JEE MAIN 2019, Diffcult
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$g_{e f f}=\sqrt{g^{2}+\left(\frac{q E}{m}\right)^{2}}$
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A point electric dipole placed at the origin has a potential given by $V(r, \theta)=\frac{p \cos \theta}{4 \pi \varepsilon_0 r^2}$, where $\theta$ is the angle made by the position vector with the direction of the dipole. Then,
The plates of a capacitor are charged to potential difference of $V\, volts$ and then connected across a resistor. The potential difference across the capacitor decreases exponentially with respect to time. After one second, the potential difference between the plates is $V/3$; then after two seconds from the start, the potential difference between the plates is
A two point charges $4 q$ and $-q$ are fixed on the $x-$axis at $x=-\frac{d}{2}$ and $x=\frac{d}{2},$ respectively. If a third point charge $'q'$ is taken from the origin to $x = d$ along the semicircle as shown in the figure, the energy of the charge will
In the figure, the inner (shaded) region $A$ represents a sphere of radius $r_A=1$, within which the electrostatic charge density varies with the radial distance $r$ from the center as $\rho_A=k r$, where $k$ is positive. In the spherical shell $B$ of outer radius $r_B$, the electrostatic charge density varies as $\rho_{\bar{B}}=\frac{2 k}{r}$. Assume that dimensions are taken care of. All physical quantities are in their $SI$ units.
Which of the following statement($s$) is(are) correct?
The distance between the circular plates of a parallel plate condenser $40\,mm$ in diameter, in order to have same capacity as a sphere of radius $1\;metre$ is....$mm$
Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance $C$ if the equivalent capacitance between point $A$ and $B$ is to be $1\,\mu F$ is