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Electric Charges And Fields

Question

A charge q is placed at the centre of the line joining two equal charges Q. Show that the system of three charges will be in equilibrium if q = – Q / 4.

Solution

Let two equal charges Q each, be held at A and B, where AB = 2x.
C is the centre of AB, where charge q is held, figure below.

Net force acting on q is zero. So q is already in equilibrium.
For the three charges to be in equilibrium, net force on each charge must be zero.

Now, total force on Q at B due to q and Q at A is

$\frac{1}{4 π \in_{0}} \frac{Q q}{x^{2}} + \frac{1}{4 π \in_{0}} \frac{QQ}{(2 x)^{2}} = 0$

$\Rightarrow$ $\frac{1}{4 π \in_{0}} \frac{Qq}{x^{2}} = - \frac{1}{4 π \in_{0}} \frac{Q Q}{(2 x)^{2}} = 0$

$\Rightarrow$ $q = - \frac{Q}{4}$

Hence proved.

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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Electric Charges And Fields

A charge q is placed at the centre of the line joining two equal charges Q. Show that the system of three charges will be in equilibrium if q = – Q / 4.

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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For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

A charge q is placed at the centre of the line joining two equal charges Q. Show that the system of three charges will be in equilibrium if q = – Q / 4.

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

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?