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  4. Three charges of each magnitude 100 μ C are placed at the corners A, B and C of an equilateral triangle of side 4 m. If the charges at points A and C are positive and the charge at point B is negative, then the magnitude of total force acting on the charge at C and angle made by it with AC are

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Q. Three charges of each magnitude $100 \, \mu C$ are placed at the corners $A, B$ and $C$ of an equilateral triangle of side $4 m$. If the charges at points $A$ and $C$ are positive and the charge at point $B$ is negative, then the magnitude of total force acting on the charge at $C$ and angle made by it with $AC$ are

AP EAMCETAP EAMCET 2019

Solution:

According to the question, we can draw the following diagram,
image
From the question, it clear that the charge on the each corner is $100 \,\mu C$.
So, $F_{net } =F $
$=\frac{k Q_{1} Q_{2}}{r^{2}}\,\,\,\,\,\,\dots(i)$
Given, $Q_{1}=Q_{2}=100 \,\mu C =100 \times 10^{-6} \,C $,
$\left[ 1\, \mu C =10^{-6} C \right]$
and $r=4 \,m$
Putting the given values in Eq. (i), we get
$=\frac{9 \times 10^{9} \times\left(100 \times 10^{-6}\right)^{2}}{(4)^{2}} $
$F_{\text {net }} =5.625 \,N$ ,
$60^{\circ}$