Two fixed point charges + 4e and + e units are separated by a distance a. Where should the third point charge be placed for it to be in equilibrium?

Solution

Let a point charge q be held at a distance x from the charge + 4e in between the charges e and 4e.

∴ Distance of q from charge + e = (a – x)
Force on charge exerted by the charge + 4e is

F_{1} = \frac{q (4 e)}{4 π \in_{0} x^{2}}

[directed away from (4e)]

Force on charge q exerted by the charge + e is

F_{2} = \frac{q (e)}{4 π \in_{0} (a - x)^{2}},

[directed away from (e)]

For the charge q to be in equilibrium F₁ = F₂

i.e.,

\frac{q (4 e)}{4 π \in_{0} x^{2}} = \frac{q (e)}{4 π \in_{0} (a - x)^{2}}

\Rightarrow \frac{4}{x^{2}} = \frac{1}{(a - x)^{2}} \Rightarrow \frac{2}{x} = \frac{1}{a - x}

∴

x = 2 a - 2 x

3 x = 2 a \Rightarrow x = 2 a / 3

Hence the charge q should be held at a distance 2a / 3 from charge (+ 4e) and a/3 from charge (e).

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Electric Charges And Fields

Two fixed point charges + 4e and + e units are separated by a distance a. Where should the third point charge be placed for it to be in equilibrium?

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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For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

Two fixed point charges + 4e and + e units are separated by a distance a. Where should the third point charge be placed for it to be in equilibrium?

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?