# Superposition principle | electric field due to system of Charges.

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# SUPERPOSITION PRINCIPLE OF ELECTRIC FIELD

Today we are going to talk about superposition principle of electric field, in the previous article we have discussed about superposition principle of electrostatic force.
So let’s discuss about today’s topic –
Consider a system of n Charges q1, q2, q3 …. and ….. qn. Which are surrounded around a test charge q0 which is at point P at different distances r1, r2, r3 ….  and rn.  According to the Coulomb’s Law, this system of Charges will exert electrical force on the test charge q0.
Let’s take F1, F2, F3 ….. and …..Fn are the forces on the test charge q0 by the charges q1, q2, q3 …. and ….. qn.
If Fi is the force due to i(th) charge qi on q0 then Fi will be –
Fi = (qiq0/4πε0.r²i)ri
Where ri is the distance between test charge q0 and qi.
The electric field Ei due to charge qi at distance ri is given as –
Ei = Fi/q0 = (qiq0/4πε0.r²i.q0)ri
Or                     Ei = (qi/4πε0.r²i)ri
If E is the total electric field at point P due to the system of n Charges then the superposition principle of electric field says that – Electric field on any charge due to numbers of other charges is the vector sum of all the electric field on that charge due to the other charges taken at a time.
The individual electric field remains unaffected by the presence of other charges.
Mathematically it is given as –
Put the value of Ei in the above equation, then we get –
So this is the required value of electric field due to system of Charges with the help of superposition principle.
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