Question

19. (a) Consider a system of n charges q, q2, ... q, with
position vectors 7, 72, 73, ... To relative to some
origin 'O'. Deduce the expression for the net
electric field É at a point P with position vector
To, due to the system of charges.​

Answer 1

Given:

A system of n charges q.

The position vectors of these charges are T1, T2, T3,...Tn, relative to origin.

To Find:

The expression for the net  electric field É at a point P with position vector  To, due to the system of charges.​

Solution:

Consider single charge q.

Electric field due to this charge q  at T0 is,

• E = $\frac{1}{4\pi \epsilon_0}$ $\frac{q}{|T1- T0|^{2} }$ (T0 - T1) , along vector T0 -T1 .

Similarly we can add the Electric fields due to all the charges as,

• E = $\frac{q}{4\pi\epsilon_0}$  ∑$\frac{ T0 - Ti}{| T0 - Ti|^{2}}$

The expression for the net  electric field É at a point P with position vector  To, due to the system of charges is  E =  $\frac{q}{4\pi\epsilon_0}$   ∑$\frac{ T0 - Ti}{| T0 - Ti|^{2}}$  i = 1,2,3,...n.