Unit 1-2: Electric Field Study Notes

Definition: An electric field exists in space around a charged object and exerts force on other charges within that region.
Electric Field Strength ( $E$ ): Defined as the electric force ( $F$ ) acting on a positive test charge ( $q_0$ ) divided by the magnitude of that charge: * $E = \frac{F}{q_0}$
Field of a Point Charge: The magnitude at a distance $r$ from a charge $q$ is calculated as: * $E = k \frac{q}{r^2} \hat{r}$
Superposition Principle: The field due to multiple source charges is the vector sum: * $E = \sum E_i = k \sum \frac{q_i}{r_i^2} \hat{r}_i$
Units and Vector Nature: The electric field is a vector quantity with units of Newtons per Coulomb ( $N/C$ ).

Electrostatic Equilibrium: A state where excess charge has distributed itself to minimize repulsive forces.
Properties of Conductors in Equilibrium: 1. The electric field is zero everywhere inside the conductor ( $E = 0$ ). 2. Any excess charge resides exclusively on the surface. 3. Electric field lines just outside the surface are perpendicular to it. 4. On non-uniform conductors, charge concentration is highest at locations of greatest curvature.
Electrical Shielding: A neutral hollow metal box (Faraday cage) cancels external fields within its interior, protecting sensitive instruments.

Function: Provide a visual representation of field direction and strength.
Drawing Rules: * Lines originate from positive charges and terminate on negative charges (or infinity). * The vector $E$ is tangent to the field line at any point. * Density of lines is proportional to field magnitude ( $E$ is larger where lines are closer). * Field lines never cross.
Specific Configurations: * Electric Dipole: A pair of equal and opposite charges. * Parallel Plate Capacitor: Produces a uniform field ( $E = \frac{V}{d}$ ) where lines are parallel and equally spaced, except near the edges. * Null Point: A location where the resultant electric field is zero.

Acceleration: A particle of charge $q$ and mass $m$ in a uniform field $E$ experiences constant acceleration: * $a = \frac{qE}{m}$
Direction: Positive particles accelerate in the direction of the field; negative particles accelerate in the opposite direction.
Millikan’s Oil-Drop Experiment: Used to measure the elementary charge ( $e$ ) by balancing oil droplets in an electric field.

Natural Phenomena: Lightning occurs due to strong atmospheric electric fields.
Medical and Industrial Use: * Electrical stimulation is used to restore muscular functionality or suppress neural activity. * Particle accelerators use electric fields to propel elementary particles to high energies for research (nuclear physics), medical diagnosis (radioisotopes), and industrial sterilization.

Is the electric field a vector or scalar? Vector.
What are the units of the electric field? $N/C$ .
Calculation: A $2\,C$ charge experiences a $40\,N$ force. What is the field? $20\,N/C$ .
Calculation: At $2\,m$ from charge $Q$ , the field is $20\,N/C$ . What force does a $5\,C$ charge feel? $100\,N$ .
Example 1 Result: For $Q = -3.0 \times 10^{-6}\,C$ at $r = 0.30\,m$ , field strength is $3.0 \times 10^5\,N/C$ directed toward the charge.
Example 4 Result: An electron in a $200\,N/C$ field experiences an acceleration of $-3.5 \times 10^{13}\,m/s^2$ . For a horizontal distance of $0.100\,m$ and $v_i = 3.0 \times 10^6\,m/s$ , the vertical displacement is $-1.94\,cm$ .