AcademyElectric Charge and Fields
Academy
Electric Fields and Forces
Level 1 - Physics topic page in Electric Charge and Fields.
Principle
An electric field is the force per unit positive test charge at a point in space.
Notation
\(\vec E\)
electric field
\(\mathrm{N\,C^{-1}}\)
\(q_0\)
small positive test charge
\(\mathrm{C}\)
\(q\)
charge placed in the field
\(\mathrm{C}\)
\(\vec F\)
electric force
\(\mathrm{N}\)
\(\vec a\)
acceleration of a charged particle
\(\mathrm{m\,s^{-2}}\)
Method
Derivation 1: Define the field at a point
To describe the source charges without building a new force problem for every possible test charge, divide the force on a small positive test charge by that test charge.
Force on test charge
\[\vec F_0=q_0\vec E\]
Field definition
\[\vec E=\frac{\vec F_0}{q_0}\]
\(q_0\) is taken small enough that it does not rearrange the source charges.
Field direction
\[\vec E\ \text{points in the force direction on a positive test charge}\]
Derivation 2: Put any charge in the field
Once the field is known, the force on a charge is proportional to its charge. Negative charges accelerate opposite the field direction.
Force law
\[\vec F=q\vec E\]
Newton's second law
\[m\vec a=q\vec E\]
Charged-particle acceleration
\[\vec a=\frac{q}{m}\vec E\]
Rules
These are the compact field-force relations.
Field definition
\[\vec E=\frac{\vec F_0}{q_0}\]
Force from field
\[\vec F=q\vec E\]
Field units
\[1\,\mathrm{N\,C^{-1}}=1\,\mathrm{N}/\mathrm{C}\]
Particle acceleration
\[\vec a=\frac{q}{m}\vec E\]
Examples
Question
A
\[+4.0\,\mathrm{nC}\]
charge experiences a \[2.0\times10^{-5}\,\mathrm{N}\]
force to the right. Find the electric field.Answer
\[E=\frac{F}{q}=\frac{2.0\times10^{-5}}{4.0\times10^{-9}}=5.0\times10^3\,\mathrm{N\,C^{-1}}\]
The field points right because the charge is positive.Checks
- Field direction is defined by the force on a positive test charge.
- A negative charge feels force opposite \(\\vec E\).
- The field exists at a point even before a test charge is placed there.
- Electric field is a vector, so components and signs matter.