The escape speed of an electron launched from the surface of a glass sphere of diameter $1 \ cm$ that has been charged to $10 \ nC$ is $x \times 10^7 \ m/s$. The value of $x$ is:

$A$ regular hexagon with side length '$a$' is shown. Find the electric field and electric potential at point '$A$'.

While working on a physics project at a school physics lab,you require a $4 \,\mu F$ capacitor in a circuit across a potential difference of $1 \,kV$. Unfortunately,$4 \,\mu F$ capacitors are out of stock in your lab,but $2 \,\mu F$ capacitors which can withstand a potential difference of $400 \,V$ are available in plenty. If you decide to use the $2 \,\mu F$ capacitors in place of the $4 \,\mu F$ capacitor,what is the minimum number of capacitors required?

$A$ circuit is connected as shown in the figure with the switch $S$ open. When the switch is closed,the total amount of charge that flows from $Y$ to $X$ is

In the given circuit,a charge of $+80 \ \mu C$ is given to the upper plate of the $4 \ \mu F$ capacitor. Find the charge on the upper plate of the $3 \ \mu F$ capacitor in the steady state in $\mu C$.

$A$ parallel plate capacitor of capacity $C_0$ is charged to a potential $V_0$. $(i)$ The energy stored in the capacitor when the battery is disconnected and the plate separation is doubled is $E_1$. (ii) The energy stored in the capacitor when the charging battery is kept connected and the separation between the capacitor plates is doubled is $E_2$. Then,the value of $E_1 / E_2$ is: