Three identical uncharged metal spheres are at the vertices of an equilateral triangle. One at a time, a small sphere is connected by a conducting wire with a large metal sphere that is charged. The center of the large sphere is in the straight line perpendicular to the plane of equilateral triangle and passing through its centre (see figure). As a result, the first small sphere acquires charge $q_1$ and second charge $q_2 (q_2 < q_1)$ . The charge that the third sphere $q_3$ will acquire is (Assume $l >> R$ , $l >> r$ , $d >> R$ , $d >> r$ )
$\frac{{q_1^2}}{{{q_2}}}$
$\frac{{q_2^2}}{{{q_1}}}$
$\sqrt {{q_1}{q_2}} $
$\frac{{{q_1} + {q_2}}}{2}$
Two charges $+q$ and $-3q$ are placed on $x-$ axis separated by a distance $d$. ($-3q$ is right of $q$) Where should a third charge $2q$ be placed such that it will not experience any force ?
What is the equivalent capacitance of the system of capacitors between $A$ and $B$ :-
A metallic shell has a point charge $'q'$ kept inside its cavity. Which one of the following diagrams correctly represents the electric field lines
A capacitor $C = 100$ $ \mu F$ is connected to three resistors each of resistance $1$ $kW$ and a battery of emf $9$ $V$. The switch $S $ has been closed for long time so as to charge the capacitor. When switch $S $ is opened, the capacitor discharges with time constant.....$ms$
Side length of equilateral triangle is $d. P$ is mid of side then potential at point $P, V_P$ is