Question

Six point charges are kept at the vertices of a regular hexagon of side $L$ and centre $O$, as shown in the figure. Give that $K=\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{L^{2}}$, which of the following statement(s) is (are) correct?

• A. The electric field at O is 6 K along OD.
• B. The potential at O is zero.
• C. The potential at all points on the line PR is same.
• D. The potential at all points on the line ST is same.

Answer 1

Answer: (A), (B), (C)

It can be seen, from the figure depicted here, that $\left|\vec{E}_{34}\right|=\left|\vec{E}_{12}\right|=2 K$.
Therefore, $\vec{E}_{34}+\vec{E}_{12}=\vec{E}^{\prime}=2 K$ is along $OD$.
Also the net field $\vec{E}=\vec{E}^{\prime}+\vec{E}_{56}$
$=2 K +4 K =6 K$ is along $OD$.

The three sets of the dipoles create a zero potential at the centre.
The vertical line $PR$ is along the equatorial axis of three sets of dipoles.
Now, the potential at all points along the line $PR$ is zero.
The line $ST$ lies along the axis of the dipole $(+2 q,-2 q)$ and the potential varies from point to point.