Consider a very long cylinder of radius $a$ having a uniform positive charge density $\rho$. A sphere of radius $a$ has been carved out (see figure), leaving no charge in that region. The distance radially outward to the cylinder, as measured from the center of the sphere is $x$. At what value of $x$ will the electric field be maximum?

Consider that in a fission of a single Plutonium ( $\mathrm{Pu}^{239}$ ) atom 207 MeV energy is released. Assuming all atoms of Plutonium undergo fission, which of the following options is the closest estimate of the amount of Plutonium required for a 20,000 units of TNT explosion? (1 unit of TNT $=4.184 \times 10^9 \mathrm{~J}, 1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}$ )

In the given circuit, the box $B$ either contains a capacitor, or an inductor or a resistor. The current $I$ versus time $t$ plots for three cases $\left(a_1, a_2, a_3\right)$ are shown in figures. The switch $S$ is closed at time $t=0$. Which of the following is correct?

In the given circuit each of the resistors is of $1 \mathrm{k} \Omega$ resistance and each of the capacitors has $4 \mu \mathrm{~F}$ capacitance. What is the charge in the capacitor between the points B and F ?