Contact and non-contact forces
A force is a push or a pull. A contact force needs touch: friction, a kick, the push of a table on a book. A non-contact force works across a gap. There are three you meet every day:
- Gravity: every mass pulls every other mass. It is always attractive.
- Electric force: charges pull or push. Opposite charges attract; like charges repel.
- Magnetic force: magnets pull or push. Opposite poles attract; like poles repel. Magnets also attract iron, nickel and cobalt.
How can something pull without touching? We say the object is surrounded by a field.
What is a field?
A field is a region of space where an object feels a force. A mass has a gravitational field, a charge has an electric field, and a magnet or an electric current has a magnetic field.
Field lines
- The arrow on a line shows the direction of the force on a test object (a small mass, a small + charge, or the N pole of a compass).
- Lines close together = strong field. Lines far apart = weak field.
- Field lines never cross.
Field strength
Field strength = force on each unit of the test object. Gravitational field strength g = F / m (N/kg). On Earth's surface g ≈ 9.8 N/kg; on the Moon about 1.6 N/kg. Electric field strength E = F / q (N/C).
Uniform and radial fields
Near the ground, Earth's field is almost uniform (parallel lines, same strength). Far away, it is radial (lines point to the centre and spread out).
How fields change with distance
For a point mass or point charge the force follows the inverse-square law: F ∝ 1/r². Double the distance r → force ÷ 4. Triple it → force ÷ 9.
- Newton's law of gravity: F = G m₁m₂ / r²
- Coulomb's law: F = k q₁q₂ / r²
A field stores energy. When you lift a bag, you do work against gravity and energy is stored in the gravitational field (gravitational potential energy, mgh). Pulling apart two opposite charges or two attracting magnets also stores energy in their field. Let go, and the field turns it back into kinetic energy.
The four fundamental forces
Every force, even friction and a push, comes from just four basic forces:
- Gravity: weakest, but long-range and always attractive. Holds planets and galaxies.
- Electromagnetic force: electric + magnetic together. Holds atoms and molecules; causes friction, tension and contact forces.
- Strong nuclear force: strongest, very short range. Holds protons and neutrons in the nucleus.
- Weak nuclear force: very short range; causes some radioactive decay (beta decay) and helps the Sun shine.
Key formulas and definitions
- [object Object]
- [object Object]
- [object Object]
- [object Object]
- [object Object]
Worked examples
1. A 5 kg bag is on Earth (g = 9.8 N/kg). What is its weight?
Weight = m × g = 5 × 9.8 = 49 N.
2. A satellite feels 800 N of gravity at distance r from Earth's centre. What does it feel at 2r?
Force ∝ 1/r². At 2r, force = 800 / 2² = 800 / 4 = 200 N.
3. A charge of 2 C feels a force of 10 N in an electric field. What is the field strength?
E = F / q = 10 / 2 = 5 N/C.
Common mistakes
- Thinking gravity needs air to work. Fields work in empty space too: the Moon pulls the oceans across space.
- Thinking field lines are real strings. They are a drawing that shows the direction and strength of the force.
- Halving the force when distance doubles. The inverse-square law makes it one quarter.
- Mixing up mass and weight. Mass is in kg; weight is a force in newtons: W = mg.