Consider a system of charges `q_1, q_2, ..., q_n` with position vectors `r_1,
r_2, ..., r_n` relative to some origin O. Like the electric field at a point in
space due to a single charge, electric field at a point in space due to the
system of charges is defined to be the force experienced by a unit
test charge placed at that point, without disturbing the original
positions of charges `q_1, q_2, ..., q_n.` We can use Coulomb-s law and the
superposition principle to determine this field at a point P denoted by
position vector r.
Electric field `E_1` at r due to `q_1` at `r_1` is given by :
`E_1 = 1/(4pi epsilon_0)(q_1)/r_(1P)^2 hat(r_(1P))`
where `hat(r_(1P))` is a unit vector in the direction from `q_1` to `P,` and `r_(1P)` is the distance between `q_1` and `P`. In the same manner, electric field `E_2` at r due to `q_2` at `r_2` is
`E_2 = 1/(4pi epsilon_0)(q_2)/r_(2P)^2 hat(r_(2P))`
where `hat(r_2P)` is a unit vector in the direction from `q_2` to P and `hat(r_(2P))` is the distance between `q_2` and P. Similar expressions hold good for fields `E_3, E_4, ..., E_n ` due to charges `q_3, q_4, ..., q_n.` By the superposition principle, the electric field E at r due to the system of charges is in Fig.
`E(r) = E_1(r) + E_2(r) + E_3(r) +........+ E_n(r)`
`= 1/(4pi epsilon_0)(q_1)/r_(1P)^2 hat(r_(1P)) + 1/(4pi epsilon_0)(q_2)/r_(2P)^2 hat(r_(2P)) +...........+ 1/(4pi epsilon_0)(q_n)/r_(nP)^2hat(r_(nP))`
`E(r)= 1/(4pi epsilon_0)sum_(i= 1)^n (q_i)/r_(iP)^2 hat(r_(iP))`
E is a vector quantity that varies from one point to another point in space and is determined from the positions of the source charges.
Consider a system of charges `q_1, q_2, ..., q_n` with position vectors `r_1,
r_2, ..., r_n` relative to some origin O. Like the electric field at a point in
space due to a single charge, electric field at a point in space due to the
system of charges is defined to be the force experienced by a unit
test charge placed at that point, without disturbing the original
positions of charges `q_1, q_2, ..., q_n.` We can use Coulomb-s law and the
superposition principle to determine this field at a point P denoted by
position vector r.
Electric field `E_1` at r due to `q_1` at `r_1` is given by :
`E_1 = 1/(4pi epsilon_0)(q_1)/r_(1P)^2 hat(r_(1P))`
where `hat(r_(1P))` is a unit vector in the direction from `q_1` to `P,` and `r_(1P)` is the distance between `q_1` and `P`. In the same manner, electric field `E_2` at r due to `q_2` at `r_2` is
`E_2 = 1/(4pi epsilon_0)(q_2)/r_(2P)^2 hat(r_(2P))`
where `hat(r_2P)` is a unit vector in the direction from `q_2` to P and `hat(r_(2P))` is the distance between `q_2` and P. Similar expressions hold good for fields `E_3, E_4, ..., E_n ` due to charges `q_3, q_4, ..., q_n.` By the superposition principle, the electric field E at r due to the system of charges is in Fig.
`E(r) = E_1(r) + E_2(r) + E_3(r) +........+ E_n(r)`
`= 1/(4pi epsilon_0)(q_1)/r_(1P)^2 hat(r_(1P)) + 1/(4pi epsilon_0)(q_2)/r_(2P)^2 hat(r_(2P)) +...........+ 1/(4pi epsilon_0)(q_n)/r_(nP)^2hat(r_(nP))`
`E(r)= 1/(4pi epsilon_0)sum_(i= 1)^n (q_i)/r_(iP)^2 hat(r_(iP))`
E is a vector quantity that varies from one point to another point in space and is determined from the positions of the source charges.
