Question:

Three identical charges are placed at the vertices of an equilateral triangle. The force experienced by each charge, (if k = 1/4$\pi\varepsilon_{0}$) is

Updated On: Jun 23, 2023
  • $2k \frac{q^{2}}{r^{2}}$
  • $ \frac{kq^{2}}{2r^{2}}$
  • $\sqrt{3}\,k \frac{q^{2}}{r^{2}}$
  • $ \frac{kq^{2}}{\sqrt{2}r^{2}}$
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The Correct Option is C

Solution and Explanation

Force on charge q at A: $\left(i\right) \quad$ Due to B, f = kq ? $\frac{q}{r2}$ or $f=\frac{kq^{2}}{r^{2}}$ along BA $\left(ii\right)\quad$ Due to C, $f=\frac{kq^{2}}{r^{2}}$ along CA $\therefore\quad$ Resultant force = F $F^{2}=f^{ 2}+f^{ 2}+2f \times f \times cos 60^{\circ}$ $F^{2}=2f^{ 2}+\frac{2f^{ 2}\times1}{2}=3f^{ 2}$ or $\quad F=\sqrt{3}f$ or$\quad$ Resultant force = $\sqrt{3} \frac{kq^{2}}{r^{2}}$
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Concepts Used:

Electric charges and field

What is Electric Charge

It is the property of subatomic particles that experiences a force when put in an electric and magnetic field.

What is Electric Field

It is a property associated with each point in space when charge is present in any form. The magnitude and direction of the electric field are expressed by E, called electric field strength or electric field intensity.

Electric charges are of two types: Positive and Negative. It is commonly carried by charge carriers protons and electrons.

Properties of Electric Charge

Various properties of charge include the following :-

Types of electric charge

Two kinds of electric charges are there :-

Negative Charge - When an object has a negative charge it means that it has more electrons than protons.

Positive Charge - When an object has a positive charge it means that it has more protons than electrons.

When there is an identical number of positive and negative charges, the negative and positive charges would cancel out each other and the object would become neutral.