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 can u plz explain principle of superposition in detail ?

The superposition principle in electrostatics states that the net Coulomb force on a charge (q) due to a system of charges is the vector addition of the individual Coulomb forces on the charge.

That is, F = F 1 + F 2 + F 3 + F 4 + ……. F n 

Any individual coulomb force is independent of the coulomb forces due to the other charges in the system.

Dividing the above equation by q we get,

E = E 1 + E 2 + E 3 + E 4 + ……. E n 

Thus, the net electric field at the position of q is the vector addition of individual electric field due to the charges in the system.

Now, multiplying the above equation with the individual distances and integrating we get,

V = V 1 + V 2 + V 3 + V 4 +……….V n

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1.6 Forces between More than Two Charges: The Superposition principle
“ When more than one Coulombian force are acting on a charge, the resultant
Coulombian force acting on it is equal to the vector sum of the individual forces.”
Consider charges q1, q2 and q3 having position vectors
® ® ®
r1, r2 and r3 respectively. Let
® ®
F21 and F23 be the forces
acting on charge q2 due to charges q1 and q3 respectively.
Then, ( r - r ) and
r - r
q q
F = k
2 1
3
2 1
2 1
21
→ →
→ →
→
l l
( r - r )
r - r
q q
F = k
2 3
3
2 3
2 3
23
→ →
→ →
→
l l
and from the principle of superposition, the resultant force acting on charge q2 is
1 - ELECTRIC CHARGE AND ELECTRIC FIELD Page 4
( r - r )
r - r
q q
( r - r ) + k
r - r
q q
F = k
2 3
3
2 3
2 3
2 1
3
2 1
2 1
2
→ →
→ →
→ →
→ →
→
l l l l
and in short,
®
F2 = kq2 r r )
r r
q
2 j
3
2 j
3
j 2
j = 1
( -
-
j → →
→ →
≠
Σ
l l
In general, the force acting on charge qi due to a system of N electric charges will be
r r )
r r
q
F kq
i j
3
i j
N j
j i
i i j = 1 ( -
-
→ → →
→ →
≠
Σ
l l
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the superposition principle helps one to calculate a certain quantity (say potential at a point due to many point charges) by simply adding up the individual potentials made by each charges at the specified point.  So, actually it makes our work simpler as we need not use vectors to solve this.   Otherwise , we need to use the vector rules (triangle law, parallelogram law etc.) to solve the problem.  

So in physics, if there is any superposition principle is used, we can easily understand that, the physical term or quantity we are dealing is not a vector but a scalar quantity which can be easily add or substract and no need for any vector rules.

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acc. to it the force exerted on a test charge by a large no. of particles is equal to the vector sum of forces exerted by all the individual particles on that test charge

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