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Electric & Magnetic
Field Models

Understand how charges create electric fields and moving charges produce magnetic fields: the invisible forces that shape our universe.

High School Physics

What Is a Field?

A field is a region of space where a force acts on an object without physical contact. Instead of thinking about charges "reaching out" to push each other, we say each charge creates a field that fills the surrounding space.

Electric Field
Created by electric charges (positive or negative). Exerts force on other charges placed in the field.
Magnetic Field
Created by moving charges (electric currents). Exerts force on other moving charges or magnetic materials.

The Electric Field \(\vec{E}\)

An electric field \(\vec{E}\) describes the force per unit charge at every point in space around a source charge. A small positive test charge \(q_0\) placed in the field experiences a force:

+
\(\vec{E}\)
Field lines point away from + charge

Reading Field Lines

1
Direction: Lines point in the direction a positive test charge would move: away from \(+\), toward \(-\).
2
Density: Closer lines = stronger field. Spread-out lines = weaker field.
3
No crossing: Field lines never intersect. At any point in space, the field has exactly one direction.
4
Start and end: Lines begin on positive charges and terminate on negative charges (or extend to infinity).

Coulomb's Law: The Core Rule

The electric force between two point charges is given by Coulomb's Law. Combined with the field definition, it gives the electric field of a point charge:

\(+q_1\)
\(-q_2\)
\(r\)
\(F\) on \(q_1\)
\(F\) on \(q_2\)

The Magnetic Field \(\vec{B}\)

A magnetic field \(\vec{B}\) is produced by moving charges (electric currents). Unlike electric fields, magnetic field lines form closed loops: they never start or end on a charge.

\(I\)
\(\vec{B}\)
B-field loops around current \(I\) (out of page)

Electric vs Magnetic Fields

Property Electric Field \(\vec{E}\) Magnetic Field \(\vec{B}\)
Source Electric charges (+ or −) Moving charges / currents
Acts on Any charge (stationary or moving) Only moving charges
Field lines Begin on +, end on − Closed loops (no start/end)
Force direction Along field lines Perpendicular to \(\vec{v}\) and \(\vec{B}\)
Key equation \(\vec{F} = q\vec{E}\) \(F = qvB\sin\theta\)

Force on a Moving Charge

A charge \(q\) moving with velocity \(\vec{v}\) through a magnetic field \(\vec{B}\) experiences a force given by:

\(\theta = 90^\circ\)
Maximum force: \(F = qvB\). The charge moves perpendicular to the field.
\(\theta = 0^\circ\)
Zero force: \(F = 0\). The charge moves parallel to the field.
Direction
Force is always perpendicular to both \(\vec{v}\) and \(\vec{B}\) (use right-hand rule).

How to Model a Field Problem

1
Identify the source: Is the field caused by a charge (electric) or a current (magnetic)?
2
Choose the law: Use \(E = k|q|/r^2\) for electric fields, or apply the right-hand rule for magnetic fields.
3
Draw field lines: Sketch the field pattern. For \(\vec{E}\): radial lines from charges. For \(\vec{B}\): loops around the current.
4
Determine force: Place a test charge or moving charge and find the force direction: \(\vec{F} = q\vec{E}\) or \(\vec{F} = q\vec{v} \times \vec{B}\).
5
Check units and signs: Verify your answer has correct units and that the force direction is consistent with charge sign.

Example 1: Electric Field of a Point Charge

A charge \(q = +3.0 \;\mu\text{C}\) is located at the origin. Find the electric field at a point \(r = 0.50 \;\text{m}\) away.

\(+3 \mu\text{C}\)
P
\(r = 0.50\) m
\(\vec{E}\)

Example 2: Magnetic Force on a Proton

A proton (\(q = 1.6 \times 10^{-19}\;\text{C}\)) moves at \(v = 5.0 \times 10^6\;\text{m/s}\) perpendicular to a uniform magnetic field \(B = 0.20\;\text{T}\). Find the force on the proton.

Example 3: Superposition of Electric Fields

Two charges \(q_1 = +2\;\mu\text{C}\) and \(q_2 = -2\;\mu\text{C}\) are separated by \(d = 0.40\;\text{m}\). Find the net \(\vec{E}\) at the midpoint.

\(+2 \mu\text{C}\)
\(-2 \mu\text{C}\)
Midpoint
\(\vec{E}_1\)
\(\vec{E}_2\)
0.20 m
0.20 m

Fields Create Each Other

One of the most profound discoveries in physics: changing electric fields create magnetic fields, and changing magnetic fields create electric fields. This is the basis of electromagnetic waves.

Faraday's Law
A changing magnetic flux through a loop induces an electric field (and thus an EMF) in the loop.
Ampere-Maxwell
A changing electric flux (or a current) creates a magnetic field around it.

Common Mistakes to Avoid

✕ Confusing Field Direction
Electric field points away from \(+\) and toward \(-\). Do not reverse this based on the test charge sign.
✕ Forgetting \(\sin\theta\)
The magnetic force \(F = qvB\sin\theta\) depends on the angle. If \(\vec{v} \parallel \vec{B}\), the force is zero, not \(qvB\).
✕ Scalar vs Vector
Fields are vectors. When adding fields from multiple sources, use vector addition (consider directions), not just magnitudes.

Key Formulas Summary

Quantity Formula Units
Electric force \(F = k\dfrac{|q_1 q_2|}{r^2}\) \(\text{N}\)
Electric field \(E = k\dfrac{|q|}{r^2}\) \(\text{N/C}\) or \(\text{V/m}\)
Force from \(\vec{E}\) \(\vec{F} = q\vec{E}\) \(\text{N}\)
Magnetic force \(F = qvB\sin\theta\) \(\text{N}\)

Question 1 of 5

Electric field lines around a negative point charge point:

Question 2 of 5

A proton moves parallel to a uniform magnetic field \(\vec{B}\). What is the magnetic force on the proton?

Question 3 of 5

If you double the distance \(r\) from a point charge, the electric field strength \(E\):

Question 4 of 5

Which of the following best distinguishes magnetic field lines from electric field lines?

Question 5 of 5

An electron (\(q = -1.6 \times 10^{-19}\;\text{C}\)) moves at \(v = 3.0 \times 10^6\;\text{m/s}\) perpendicular to a \(B = 0.50\;\text{T}\) field. What is the magnitude of the magnetic force?