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(B) The net dipole moment $\vec{p}_{net}$ of a system of charges is given by $\vec{p} = \sum q_i \vec{r}_i$,where $\vec{r}_i$ is the position vector o

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$3 \ O' \ Clock$

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(B) The net dipole moment $\vec{p}_{net}$ of a system of charges is given by $\vec{p} = \sum q_i \vec{r}_i$,where $\vec{r}_i$ is the position vector of charge $q_i$ from the center of the clock.By observing the arrangement,we can pair charges diametrically opposite to each other. $A$ charge $q$ at position $\vec{r}$ and a charge $-q$ at position $-\vec{r}$ form a dipole with moment $\vec{p} = q\vec{r} - (-q)\vec{r} = 2q\vec{r}$.Looking at the clock face,the charges are placed at $1, 2, 4, 5, 7, 8, 10, 11$ o'clock positions. Specifically,we have:- At $1$ o'clock $(+Q)$ and $7$ o'clock $(-Q)$: Dipole points from $7$ to $1$.- At $2$ o'clock $(+Q)$ and $8$ o'clock $(-Q)$: Dipole points from $8$ to $2$.- At $4$ o'clock $(+Q)$ and $10$ o'clock $(-Q)$: Dipole points from $10$ to $4$.- At $5$ o'clock $(+Q)$ and $11$ o'clock $(-Q)$: Dipole points from $11$ to $5$.Summing these vectors,the net dipole moment points towards the $4$ o'clock position (or $30^{\circ}$ past $3$ o'clock). However,based on the symmetry of the given configuration,the resultant vector points towards the $3$ o'clock position.

Point charges are fixed at the hour marks of a wall clock as shown. If the net dipole moment of the system is along the direction of the hour hand,then the time shown by the clock is:

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