
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?

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: -
Where,
K is the Coulomb’s constant
are the charges
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,
Now, let us calculate the force on first particle 1 say with charge q as shown in the figure below.
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 is the resultant of repulsive force on particle 1 by 2 say force and attractive force by 3 on 1 say force
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
After substituting the values
We get,
Let,
…………………………….. (1)
Therefore,
……………….. (2)
Similarly, for force
After substituting values,
We get,
……………. (since charge on particle 3 is negative)
……………… (3)
Similarly, if we calculate the magnitude of other forces say
We will get the same result
Therefore,
………………. (4)
Now we know that is the resultant of and . Also, the angle between the two forces is 120 degrees.
Therefore, from (2) and (3)
We get,
On solving
We get,
…………… (since ) ……………….. (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
Therefore,
……………………………………. (B)
Now, for charge 3, we can say that angle between the component vector force say and of force is 60 degrees .
Therefore, the magnitude resultant force after substituting values of and will be given by,
On solving
We get,
………………… (since ) …………… (C)
Now, from (1) we know that
Therefore, from (1), (A) and (B)
We get,
Also from (1) and (C
We get,
Therefore, force on charged particle q, q and –q is , , respectively.
Note:
The Coulomb’s constant k is given as,
Where, is the vacuum electric permittivity. The value of k is generally taken as
Formula Used: -
Where,
K is the Coulomb’s constant
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,
Now, let us calculate the force on first particle 1 say

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
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
After substituting the values
We get,
Let,
Therefore,
Similarly, for force
After substituting values,
We get,
Similarly, if we calculate the magnitude of other forces say
We will get the same result
Therefore,
Now we know that
Therefore, from (2) and (3)
We get,
On solving
We get,
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
Therefore,
Now, for charge 3, we can say that angle between the component vector force say
Therefore, the magnitude resultant force
On solving
We get,
Now, from (1) we know that
Therefore, from (1), (A) and (B)
We get,
Also from (1) and (C
We get,
Therefore, force on charged particle q, q and –q is
Note:
The Coulomb’s constant k is given as,
Where,
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