Calculate potential energy of a point charge $-q$ placed along the axis due to a charge $+ Q$ uniformly distributed along a ring of radius $R$. Sketch $P.E.$ as a function of axial distance $z$ from the centre of the ring. Looking at graph, can you see what would happen if $-q$ is displaced slightly from the centre of the ring (along the axis) ?

Two points $P$ and $Q$ are maintained at the potentials of $10\  V$ and $- 4\ V$, respectively. The work done in moving $100$ electrons from $P$ to $Q$ is

An electron (charge = $1.6 \times {10^{ – 19}}$ $coulomb$) is accelerated through a potential of $1,00,000$ $volts$. The energy required by the electron is

On moving a charge of $20$ coulombs by $2 \;cm , 2 \;J$ of work is done, then the potential difference between the points is (in $volt$)

Figures $(a)$ and $(b)$ show the field lines of a positive and negative point charge respectively

$(a)$ Give the signs of the potential difference $V_{ P }-V_{ Q } ; V_{ B }-V_{ A }$

$(b)$ Give the sign of the potential energy difference of a small negative charge between the points $Q$ and $P ; A$ and $B$.

$(c)$ Give the sign of the work done by the field in moving a small positive charge from $Q$ to $P$.

$(d)$ Give the sign of the work done by the external agency in moving a small negative charge from $B$ to $A$.

$(e)$ Does the kinetic energy of a small negative charge increase or decrease in going from $B$ to $A?$