Electric Field Formula: The electric field (E) is calculated as the electric force (F) divided by the magnitude of a tiny test charge (Q): ( E = \frac{F}{Q} ).
Units: Newtons per Coulomb (N/C).
Vector Nature: Electric fields are vectors, indicating direction and magnitude.
Positive test charge: Accelerates in the same direction as the electric field.
Negative test charge: Accelerates in the opposite direction to the electric field.
Electric Fields Created by Charges
Positive Charge: Electric field vectors point away from the charge.
Negative Charge: Electric field vectors point towards the charge.
Equation for Point Charge: ( E = \frac{kQ}{r^2} )
( k ) is Coulomb's constant ( 9 \times 10^9 \text{N m}^2/ ext{C}^2 ).
Q is the charge.
R is the distance from the charge.
Electric Field Examples
Effect of Placement:
Positive charge: Electric field extends outward; vectors point away.
Negative charge: Vectors point toward the charge.
Example Problem: Force and direction calculation.
A force acting north on a negative charge has an electric field pointing south.
Calculating Electric Field Magnitude and Direction
Example Calculation:
Given force and charge, calculate electric field using ( E = \frac{F}{Q} ).
Convert microcoulombs to coulombs for accuracy.
Uniform Electric Fields
Creating Uniform Fields: Using parallel plates with a battery.
Positive plate: Electric field points away.
Negative plate: Electric field points toward.
Suspension of Charges: An electric field can counteract gravitational force to suspend a charge in air.
( E \times Q = m \times g ) for equilibrium.
Electric Field and Acceleration
Acceleration of an Electron:
Electric field causes acceleration opposite to field direction for negative charges.
Use ( a = \frac{E \times Q}{m} ) for acceleration.