SATHEE: Electrostatics 2 Question 19

Electrostatics 2 Question 19

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

(2012)

(a) The electric field at $O$ is $6 K$ along $O D$

(b) The potential at $O$ is zero

(d) The potential at all points on the line $S T$ is same

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Solution:

(a,b,c)

Resultant of $2 K$ and $2 K$ (at $120^{\circ}$ ) is also $2 K$ towards $4 K$ .Therefore, net electric field is $6 K$ .

$\begin{aligned} V_{0} & = \frac{1}{4 π ε_{0}} \frac{q_{A}}{L} + \frac{q_{B}}{L} + \frac{q_{C}}{L} + \frac{q_{D}}{L} + \frac{q_{E}}{L} + \frac{q_{F}}{L} \\ = \frac{1}{4 π ε_{0} L} (q_{A} + \dots + q_{F}) = 0 \end{aligned}$

Because $q_{A} + q_{B} + q_{C} + q_{D} + q_{E} + q_{F} = 0$

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Electrostatics 2 Question 19

20. Six point charges are kept at the vertices of a regular hexagon of side L and centre O as shown in the figure. Given that K=14πε0qL2, which of the following statements(s) is(are) correct.

Solution:

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