charge $Q$ is uniformly distributed over a long rod $AB$ of length $L$ as shown in the figure. The electric potential at the point $O$ lying at distance $L$ from the end $A$ is
JEE MAIN 2013, Medium
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Electric potential is given by,
$V=\int_{L}^{2 L} \frac{k d q}{x}=\int_{L}^{2 L} \frac{1}{4 \pi \varepsilon_{0}} \frac{\left(\frac{q}{L}\right) d x}{x}=\frac{q}{4 \pi \varepsilon_{0} L} \ln (2)$
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The electric field intensity produced by the radiation coming from a $100\, W$ bulb at a distance of $3\, m$ is $E$. The electric field intensity produced by the radiation coming from $60\, W$ at the same distance is $\sqrt{\frac{x}{5}} E$. Where the value of $x=......... .$
A parallel plate air capacitor has a capacitance $C$. When it is half filled with a dielectric of dielectric constant $5$, the percentage increase in the capacitance will be......$\%$
In the following diagram the work done in moving a point charge from point $P$ to point $A, B$ and $C$ is respectively as $W_A,\, W_B$ and $W_C$, then (there is no charge nearby)
A particle of charge $q$ and mass $m$ is subjected to an electric field $E = E _{0}\left(1- ax ^{2}\right)$ in the $x-$direction, where $a$ and $E _{0}$ are constants. Initially the particle was at rest at $x=0 .$ Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is
A $4\,\mu F$ condenser is connected in parallel to another condenser of $8\,\mu F$. Both the condensers are then connected in series with a $12\,\mu F$ condenser and charged to $20\;volts$. The charge on the plate of $4\,\mu F$ condenser is......$\mu C$
Three concentric metal shells $A, B$ and $C$ of respective radii $a, b$ and $c (a < b < c)$ have surface charge densities $+\sigma,-\sigma$ and $+\sigma$ respectively. The potential of shell $B$ is