Field forces
Field Forces
Field forces are forces that act between objects that are not in physical contact with each other. These forces can act over large distances and are central to many physical phenomena. The most common examples of field forces are gravitational force, electric force, and magnetic force.
Characteristics of Field Forces
Field forces have the following characteristics:
- They can act through empty space, meaning no physical medium or contact is required.
- The strength of a field force typically decreases with increasing distance between the objects.
- They are central forces, which means they act along the line joining the centers of the two interacting bodies.
- Field forces are conservative forces, which means the work done by these forces in moving an object between two points is independent of the path taken.
Types of Field Forces
Gravitational Force
The gravitational force is a mutual force of attraction between any two masses. According to Newton's law of universal gravitation, the force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between their centers.
Formula
The gravitational force ($F_g$) between two masses ($m_1$ and $m_2$) separated by a distance ($r$) is given by:
$$ F_g = G \frac{m_1 m_2}{r^2} $$
where $G$ is the gravitational constant.
Electric Force
The electric force is the force between charged particles. Coulomb's law describes the electric force between two point charges.
Formula
The electric force ($F_e$) between two point charges ($q_1$ and $q_2$) separated by a distance ($r$) is given by:
$$ F_e = k \frac{q_1 q_2}{r^2} $$
where $k$ is Coulomb's constant.
Magnetic Force
Magnetic force is the force between moving charges or magnetic materials. The force experienced by a moving charge in a magnetic field is given by the Lorentz force law.
Formula
The magnetic force ($F_m$) on a charge ($q$) moving with velocity ($\vec{v}$) in a magnetic field ($\vec{B}$) is given by:
$$ \vec{F}_m = q(\vec{v} \times \vec{B}) $$
where $\times$ denotes the cross product.
Comparison Table
| Property | Gravitational Force | Electric Force | Magnetic Force |
|---|---|---|---|
| Acts Between | Masses | Charges | Moving charges and magnetic materials |
| Formula | $F_g = G \frac{m_1 m_2}{r^2}$ | $F_e = k \frac{q_1 q_2}{r^2}$ | $\vec{F}_m = q(\vec{v} \times \vec{B})$ |
| Proportional To | Product of masses | Product of charges | Charge, velocity, and magnetic field |
| Inversely Proportional To | Square of distance | Square of distance | Not applicable (depends on angle between $\vec{v}$ and $\vec{B}$) |
| Direction | Attractive | Attractive/Repulsive | Perpendicular to $\vec{v}$ and $\vec{B}$ |
| Range | Infinite | Infinite | Finite (depends on the magnetic field source) |
| Relative Strength | Weakest | Stronger | Strongest (under certain conditions) |
Examples
Gravitational Force Example
The gravitational force between the Earth (mass $m_1 = 5.97 \times 10^{24}$ kg) and a 1 kg mass ($m_2 = 1$ kg) at the surface of the Earth (radius $r = 6.38 \times 10^6$ m) is:
$$ F_g = G \frac{m_1 m_2}{r^2} = (6.674 \times 10^{-11} \text{ N(m/kg)}^2) \frac{(5.97 \times 10^{24} \text{ kg})(1 \text{ kg})}{(6.38 \times 10^6 \text{ m})^2} \approx 9.8 \text{ N} $$
This is the force we commonly refer to as weight.
Electric Force Example
Two point charges, $q_1 = 1 \times 10^{-6}$ C and $q_2 = -2 \times 10^{-6}$ C, are separated by a distance of $r = 0.5$ m. The electric force between them is:
$$ F_e = k \frac{q_1 q_2}{r^2} = (8.987 \times 10^9 \text{ N(m}^2\text{/C}^2)) \frac{(1 \times 10^{-6} \text{ C})(-2 \times 10^{-6} \text{ C})}{(0.5 \text{ m})^2} = -7.19 \times 10^{-2} \text{ N} $$
The negative sign indicates that the force is attractive.
Magnetic Force Example
A charge $q = 1 \times 10^{-6}$ C moving with a velocity $\vec{v} = 10^3 \text{ m/s}$ $\hat{i}$ in a magnetic field $\vec{B} = 0.5 \text{ T}$ $\hat{j}$ experiences a magnetic force:
$$ \vec{F}_m = q(\vec{v} \times \vec{B}) = (1 \times 10^{-6} \text{ C})((10^3 \text{ m/s}) \hat{i} \times (0.5 \text{ T}) \hat{j}) = (1 \times 10^{-6} \text{ C})(500 \text{ N/C}) \hat{k} = 5 \times 10^{-4} \text{ N} \hat{k} $$
The force is perpendicular to both the velocity and the magnetic field.
Field forces are fundamental to understanding a wide range of physical systems, from the motion of planets to the behavior of subatomic particles. They are also the basis for many technologies, such as electric motors, generators, and electronic devices.