SATHEE: Electrostatics 7 Question 10

Electrostatics 7 Question 10

10. Consider a system of three charges $q / 3, q / 3$ and $- 2 q / 3$ placed at points $A, B$ and $C$ respectively, as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and angle $C A B = 60^{\circ}$

$(2008, 3 M)$

(a) The electric field at point $O$ is $\frac{q}{8 π ε_{0} R^{2}}$ directed along the negative $x$ -axis.

(b) The potential energy of the system is zero

(d) The potential at point $O$ is $\frac{q}{12 π ε_{0} R}$ .

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Answer:

Correct Answer: 10. (c)

Solution:

Distance $B C = A B \sin 60^{\circ} = (2 R) \frac{\sqrt{3}}{2} = \sqrt{3} R$

$∴ | F e_{B C} | = \frac{1}{4 π ε_{0}} \frac{(q / 3) (2 q / 3)}{(\sqrt{3} R)^{2}} = \frac{q^{2}}{54 π ε_{0} R^{2}}$

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Electrostatics 7 Question 10

10. Consider a system of three charges q/3,q/3 and −2q/3 placed at points A,B and C respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB=60∘

Answer:

Solution:

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10. Consider a system of three charges $q / 3, q / 3$ and $- 2 q / 3$ placed at points $A, B$ and $C$ respectively, as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and angle $C A B = 60^{\circ}$