Electric Field Study Notes
Lecture 4 - Electric Field
Electric Field Due to a Point Charge
The electric field at a point P due to a point charge Q can be expressed as:
EP = \frac{FP}{Q} = k \frac{q}{r^{2}}
Where:
E_P = electric field at point P
F_P = force experienced at point P
k = Coulomb's constant
q = charge producing the electric field
r = distance from the charge to point P
Direction of Electric Field (E):
Points away from positive charges (+)
Points toward negative charges (-)
Electric Field Due to Multiple Charges: Superposition
Principle of Superposition:
The net electric field at a point P due to multiple source charges is the vector sum of the electric fields created by each individual charge.
Mathematically, for multiple charges:
E{net} = \sum Ei
Where each E_i represents the electric field due to the ith charge.
Source Charges:
Each of the source charges contributes its electric field at point P, necessitating the use of vector addition to find the net electric field.
Electric Field Concept Summary
A charge generates an electric field denoted as E(r), which varies based on spatial position r.
For multiple charges, the electric field at position r is a vector superposition of the fields E(ri) produced by each individual charge qi.
Note: Clarification may be needed regarding what ri signifies; visual aid may be used to illustrate this.
When a charge Q is situated at point P (position r) in the electric field created by other charges qi, it will experience an electric force calculated as:
F(r) = Q E(r)
The electric field at point P depends solely on the source charges qi and the position r, independent of charge Q.
Analogy: Similar to gravitational acceleration g which remains unaffected by the presence of a mass in the gravitational field.
A point charge does not exert a force or electric field upon itself.
Example: Electric Field Due to Two Point Charges
Setup:
Assume there are two point charges with charges +q and -q positioned at certain locations.
Electric field calculations are to be carried out at points P1 and P2 located at distances from these charges.
Calculations at Point P1
The electric field at point P1, located at coordinate x=x₁, can be calculated as:
E{P1} = k \frac{q{1}}{(x{1}+a)^{2}} + k \frac{-q{2}}{(x_{1}-a)^{2}}
This involves calculating contributions from both individual charges and summing their results.
Calculations at Point P2
The electric field at P2 positioned at coordinate y = y_1 is expressed as:
E{P2} = \sqrt{E{x}^2 + E_{y}^2}
Determine each component as follows:
E_{x} = -2k \frac{q}{r^{2}} \sin \theta
E_{y} = -|E| \cos \theta
Electric Field Lines
Electric fields can be visually represented using field lines. Characteristics of field lines include:
The direction of the lines corresponds to the direction of the electric field vector E.
The density of the field lines is proportional to the magnitude of the electric field; greater density indicates a stronger electric field.
Conceptual Practice: Sketching Electric Fields
Engage with exercises requiring the sketching of E fields at calculated points P and P’. Consider also the conceptual visualization of E fields at arbitrary points in space, especially when using identical positive charges (+q).
Strategy for Calculating Electric Fields of Charge Distributions
When faced with continuous charge distributions, the strategy involves:
Focusing on a differential charge element.
Performing integration over the entire distribution to obtain the net electric field.
Keeping in mind the symmetry of the charge distribution for simplification of calculations.