Four point charges Q, q, Q and q are placed at the corners of a square of side ‘a’ as shown in the figure
Find the
(a) resultant electric force on a charge Q,
(b) the potential energy of this system.

Solution

$F_{1} = \frac{1}{4 {πε}_{0}} = \frac{qQ}{a^{2}} F_{2} = \frac{1}{4 {πε}_{0}} \frac{qQ}{a^{2}} F_{3} = \frac{1}{4 {πε}_{0}} \frac{QQ}{(\sqrt{2 a)^{2}}} = \frac{1}{4 {πε}_{0}} \frac{Q^{2}}{2 a^{2}}$

F₁ and F₂ are perpendicular to each other so their resultant will be

$F' = \sqrt{F_{1}^{2} + F_{2}^{2} + 2 F_{1} F_{2} \cos 90^{o}} F_{1} = F_{2} F' = \sqrt{2} \frac{1}{4 {πε}_{0}} \frac{qQ}{a^{2}}$

F₃ and resultant of F₁ and F₂ will be in the same direction

Net force

F = F' + F₃

$F = \frac{Q}{4 {πε}_{0}} [\frac{\sqrt{2 q}}{a^{2}} + \frac{Q}{2 a^{2}}] = \frac{Q}{4 {πε}_{0}} [\frac{2 \sqrt{2 q} + Q}{2 a^{2}}] F = \frac{Q}{4 {πε}_{0}} [\frac{2 \sqrt{2 q} + Q}{2 a^{2}}]$

(b) The potential energy of the given system,

$W = \frac{4 KQq}{a} + \frac{{Kq}^{2}}{\sqrt{2} a} + \frac{{KQ}^{2}}{\sqrt{2} a} K = \frac{1}{4 {πε}_{0}}$

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Electric Charges And Fields

Four point charges Q, q, Q and q are placed at the corners of a square of side ‘a’ as shown in the figure
Find the
(a) resultant electric force on a charge Q,
(b) the potential energy of this system.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

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NCERT Sample Papers

Entrance Exams Preparation

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Electric Charges And Fields

Four point charges Q, q, Q and q are placed at the corners of a square of side ‘a’ as shown in the figureFind the(a) resultant electric force on a charge Q,(b) the potential energy of this system.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?b) Explain why two field lines never cross each other at any point?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Four point charges Q, q, Q and q are placed at the corners of a square of side ‘a’ as shown in the figure
Find the
(a) resultant electric force on a charge Q,
(b) the potential energy of this system.

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?