01 / 21

Energy Transfer
Via Fields

Discover how gravitational, electric, and magnetic fields store and transfer energy across space without physical contact.

High School Physics

What Is a Field?

A field is an invisible region of space where a force can act on an object without direct contact. Every charged particle, massive body, or magnet creates a field that extends outward into the surrounding space.

Gravitational
Created by any object with mass. Pulls other masses toward it.
Electric
Created by electric charges. Can attract or repel other charges.
Magnetic
Created by moving charges or magnets. Acts on other moving charges.

Fields Store Energy

A field is not just a mathematical tool: it is a physical entity that contains energy. When you separate two attracting objects or push two repelling charges together, you do work. That energy is stored in the field itself, not in the objects.

How Energy Transfers Through a Field

\(+Q\)
 Energy flows through field
\(+q\)
\(F\)
 Source Test charge

Potential Energy in Fields

When an object is positioned within a field, it possesses potential energy due to its location. This energy can be converted into kinetic energy as the field does work on the object.

Gravitational PE
\( U_g = mgh \) (near Earth's surface) or \( U_g = -\frac{GMm}{r} \) (general)
Electric PE
\( U_e = \frac{kq_1 q_2}{r} \) between two point charges separated by distance \( r \)

The Work-Energy Principle for Fields

Work done by field
\(W = Fd\)
 Change in energy KE gained = PE lost

Conservation of Energy in Fields

In an isolated system with only field forces acting, the total mechanical energy remains constant. Energy simply transforms between kinetic and potential forms.

\( KE + PE = \text{constant} \)
High up KE low PE high Midway KE med PE med Ground KE high PE low

Contact vs. Field Forces

Contact Forces Field Forces
Mechanism Physical touching Action at a distance
Examples Friction, tension, normal Gravity, electric, magnetic
Energy medium Molecular interactions Field permeating space
Range Zero (must touch) Infinite (weakens with distance)
Conservative? Usually no (friction) Yes (path-independent)

Three Types of Field Energy Transfer

1
Gravitational: A ball falls from a shelf. The gravitational field converts potential energy \( mgh \) into kinetic energy \( \frac{1}{2}mv^2 \).
2
Electric: A proton accelerates toward an electron. The electric field converts electric PE \( \frac{kq_1 q_2}{r} \) into kinetic energy.
3
Electromagnetic (radiation): Oscillating charges create electromagnetic waves that carry energy across empty space at the speed of light.

How to Analyze Field Energy Transfer

1
Identify the field: Is it gravitational, electric, or magnetic? What object creates the field?
2
Define initial and final states: Where does the object start and end? What changes in position or configuration?
3
Calculate PE at each state: Use the appropriate formula: \( mgh \), \( -\frac{GMm}{r} \), or \( \frac{kq_1 q_2}{r} \).
4
Apply conservation of energy: \( KE_i + PE_i = KE_f + PE_f \). Solve for the unknown quantity.
5
Check the direction: Energy flows from high PE to low PE. Objects accelerate along the field direction (or opposite for negative charges).

Example 1: Falling Ball

Ground
\(h = 20\) m
 2 kg
Start: \(v = 0\)
\(g\)
 2 kg
End: \(v = ?\)

Example 2: Accelerating Charge

+ −
\(V = 1000\) V
\(E\) field
\(p^+\)
 accelerates

Example 3: Energy from the Sun

Sun Electromagnetic wave Earth 150 million km of empty space No matter needed: energy travels via the field

Energy Density in Fields

The energy stored in a field can be quantified per unit volume as energy density. Stronger fields store more energy in each cubic meter of space.

Electric Field
\( u_E = \frac{1}{2}\epsilon_0 E^2 \) where \( \epsilon_0 \) is the permittivity of free space and \( E \) is the field strength.
Magnetic Field
\( u_B = \frac{B^2}{2\mu_0} \) where \( \mu_0 \) is the permeability of free space and \( B \) is the field strength.

Common Mistakes

✕ "Fields need a medium"
Unlike sound, gravitational and electromagnetic fields transmit energy through empty space: no matter is needed.
✕ Confusing force and energy
A field exerts a force, but energy transfer only occurs when the object moves. A book on a shelf has PE but no energy is transferred until it falls.
✕ Ignoring the sign of PE
Electric PE can be positive or negative depending on charge signs. Gravitational PE (\( -GMm/r \)) is always negative: forgetting this leads to wrong answers.

Field Comparison Summary

Gravitational Electric Magnetic
Source Mass Charge Moving charge
Force law \( \frac{GMm}{r^2} \) \( \frac{kq_1 q_2}{r^2} \) \( qvB\sin\theta \)
PE formula \( -\frac{GMm}{r} \) \( \frac{kq_1 q_2}{r} \) N/A (does no work)
Direction Always attractive Attract or repel Perpendicular to motion
Transfers KE? Yes Yes No (changes direction only)

Question 1 of 5

A 5 kg rock falls from rest through a height of 10 m in a gravitational field (\( g = 10 \text{ m/s}^2 \)). How much kinetic energy does it have just before hitting the ground?

Question 2 of 5

Which of the following is true about energy stored in an electric field?

Question 3 of 5

A magnetic field deflects a moving proton. What happens to the proton's kinetic energy?

Question 4 of 5

How does the Sun transfer energy to the Earth across 150 million km of empty space?

Question 5 of 5

An electron is released from rest between two charged plates with a potential difference of 500 V. What is the kinetic energy gained by the electron? (\( e = 1.6 \times 10^{-19} \text{ C} \))