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Two identical electric point dipoles have dipole moments $\overrightarrow{p}_{1}= p\hat i$ and $\overrightarrow{p}_{2}=- p\hat i$ and are held on the $x-$axis at distance $'a'$ from each other. When released, they move along the $x-$axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is $'m',$ their speed when they arc infinitely far apart is
A parallel plate capacitor is charged to a certain potential and the charging battery is then disconnected. Now, if the plates of the capacitor are moved apart then:
If a slab of insulating material $4 \times {10^{ - 3}}\,m$ thick is introduced between the plates of a parallel plate capacitor, the separation between plates has to be increased by $3.5 \times {10^{ - 3}}\,m$ to restore the capacity to original value. The dielectric constant of the material will be
A parallel plate capacitor has capacitance $C$. If it is equally filled with parallel layers of materials of dielectric constants $K_1$ and $K_2$ its capacity becomes $C_1$. The ratio of $C_1$ to $C$ is
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 plates of a parallel plate condenser is $\,4mm$ and potential difference is $60\;volts$. If the distance between the plates is increased to $12\,mm$, then
Two parallel plate condensers of capacity of $20 \mu F$ and $30 \mu F$ are charged to the potentials of $30V$ and $20V$ respectively. If likely charged plates are connected together then the common potential difference will be :-......$V$
Three concentric spherical shells have radii $a, b$ and $c (a < b < c)$ and have surface charge densities $\sigma ,-\;\sigma $ and $\;\sigma \;$ respectively. If $V_A,V_B$ and $V_C$ denote the potentials of the three shells, then, for $c = a +b,$ we have