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There is $10$ units of charge at the centre of a circle of radius $10\,m$. The work done in moving $1\, unit$ of charge around the circle once is………..$units$

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 $A?$

The displacement of a charge $Q$ in the electric field $E = {e_1}\hat i + {e_2}\hat j + {e_3}\hat k$ is $\hat r = a\hat i + b\hat j$. The work done is

$(a)$ Determine the electrostatic potential energy of a system consisting of two charges $7 \;\mu C$ and $-2\; \mu C$ (and with no external field) placed at $(-9 \;cm , 0,0)$ and $(9\; cm , 0,0)$ respectively.

$(b)$ How much work is required to separate the two charges infinitely away from each other?

$(c)$ Suppose that the same system of charges is now placed in an external electric field $E=A\left(1 / r^{2}\right) ; A=9 \times 10^{5} \;C m ^{-2} .$ What would the electrostatic energy of the configuration be?