Consider a system of n charges q1, q2,…,qn with position vectors 1, 2, 3, …, n relative to some origin ‘O’. Deduce the expression for the net electric field ⃗ at a point P with position vector p, due to this system of charges.
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Given:
A system of n charges q.
The position vectors of these charges are 1,2 ,3 , ..n, relative to origin.
To Find:
The expression for the net electric field É at a point P with position vector p, due to the system of charges.
Solution:
Consider single charge q.
Let this q be present at a position vector r.
Let 1/4π∈ = K
Electric field due to this charge q at p is,
- E = Kq/(|r- p|^{2} ) (r - p) , along vector r- p .
Similarly we can add the Electric fields due to all the charges as,
- E = K ∑ r - P/{| r - p|^{2}}
The expression for the net electric field É at a point P with position vector To, due to the system of charges is E = 1/4π∈ ∑ r - p/| r - p|^{2}, r = 1,2,3,...n.
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