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Consider the charges q, q and –q placed at the vertices of the equilateral triangle, as shown in the figure. What is the force on each charge?
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Answer
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Hint: Emissive power is the radiant energy emitted by the Body. Body should be anything either it is black or gray, coefficient of emission is the fractional part of power of a perfectly black Body at the same temperature.

Formula Used: - F=kq1q2d2
Where,
K is the Coulomb’s constant
q1q2 are the charges
d2 is the distance between the two charge

Complete step by step answer:
The electric force between two static and charged particles is called an electrostatic force. The nature of this force can be attractive or repulsive depending on whether the particles are positively/negatively charged. Coulomb’s law provides us the equation which relates the force and the charged particles along with the distance in the given charged particles.
In this question the length of the equilateral triangle is not given. Therefore, we will assume it to be l.
Now from Coulomb’s law
We know,
 F=kq1q2d2
Now, let us calculate the force on first particle 1 say F1 with charge q as shown in the figure below.
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Now, we know that particles with the same charge repel each other and that with opposite charges attract each other. Therefore, as shown in figure F1 is the resultant of repulsive force on particle 1 by 2 say force F12 and attractive force by 3 on 1 say force F13
Now for, the charge on both particles is equal in magnitude as well as direction and distance is taken as l
Therefore, Coulomb’s law can be modified as
F12=kq1q2d2
After substituting the values
We get,
F12=kq2l2
Let,
kq2l2=F…………………………….. (1)
Therefore,
|F12|=F ……………….. (2)
Similarly, for force F13
F13=kq1q2d2
After substituting values,
We get,
F13=(kq2l2) ……………. (since charge on particle 3 is negative)
|F13|=F ……………… (3)
Similarly, if we calculate the magnitude of other forces say F21,F23,F31,F32
We will get the same result
Therefore,
|F21|=|F23|=|F31|=|F32|=F ………………. (4)
Now we know that F1 is the resultant of F12 and F13. Also, the angle between the two forces is 120 degrees.
Therefore, from (2) and (3)
We get,
F1=F2+F2+2×F×Fcos120
On solving
We get,
F1=F …………… (since cos120=12) ……………….. (A)
Now, since the distance between the charge 1 and 2 is the same, also their charge and other factors such as angle and magnitude of component forces is the same. From the figure, we can say that
F1=F2
Therefore,
F2=F ……………………………………. (B)
Now, for charge 3, we can say that angle between the component vector force say F31and F32 of forceF3 is 60 degrees .
Therefore, the magnitude resultant force F3 after substituting values of F31and F32 will be given by,
F3=F2+F2+2×F×Fcos60
On solving
We get,
F3=3F………………… (since cos60 =12) …………… (C)
Now, from (1) we know that
kq2l2=F
Therefore, from (1), (A) and (B)
We get,
F2=F2=kq2l2
Also from (1) and (C
We get,
F3=3kq2l2
Therefore, force on charged particle q, q and –q is kq2l2, kq2l2, 3kq2l2 respectively.

Note:
The Coulomb’s constant k is given as,
k=14πεo
Where, εois the vacuum electric permittivity. The value of k is generally taken as k=8.9875×109N.m2/C2
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