Spring Semester 2022
Lecture 9
Fundamental problem of electrodynamics
What force do the ‘source charges’ exert on
another charge Q (test charge)?
Interaction between any two charges is
completely unaffected by presence of others
To determine the force on Q, compute
force F1 due to q1 alone (ignoring all
others), F2 due to q2 alone and so on.
𝑭 = 𝑭𝟏 + 𝑭𝟐 + 𝑭𝟑 + ⋯ .
Principle of superposition- total force on charge Q equals vector sum
of all individual forces
F depends not only on ‘r’ but also on velocity and acceleration of
charge q (only during motion)
Coulomb’s Law
Force on a test charge Q due to a single point charge q, that is
at rest, at distance ‘𝓇’ away is
𝑞𝑄
ෝ
𝑭=
𝓻
2
4𝜋𝜖0 𝓇
𝓻 = 𝒓 − 𝒓′
2
𝐶
𝜖0 = 8.85𝑥10−12
𝑁𝑚2
(permittivity of free space)
r
F = repulsive when q and Q
are of same sign
r'
Coulomb’s law + Principle of Superposition =
Physical input for electrostatics.
Electric Field
Several point charges q1, q2, ….., qn at
distances 𝓇1 , 𝓇2 , … 𝓇𝑛 from P
(principle of
𝑭 = 𝑭𝟏 + 𝑭 𝟐 + 𝑭𝟑 + ⋯
superposition)
=
1
4𝜋𝜖0
𝑞1 𝑄
𝑞2 𝑄
𝑟
ෝ
+
𝑟ෝ + ⋯
𝓇1 2 1
𝓇2 2 2
= 𝑄𝑬
(Electric field of the source
charges)
Force on charge Q is charge Q times
the electric field produced by all
different charges at P.
E is a vector quantity, varies from pointto-point, determined by configuration
of source charges. It is the force acting
on a unit charge placed at field-point P
Find the electric field a distance ‘z’ above the
midpoint of a straight line segment of length 2L
that carries the uniform line charge λ
METHOD 1
The simplest method is to chop the line into symmetrically placed pairs
at ±𝑥 and integrate 𝑥: 0 → 𝑙. But a more general approach may also be
followed as shown below:
METHOD 2