Gravity, the Electromagnetic Forces, and the Inverse Square Law

Calculating the forces between two charged particles (electric force), two magnets (the magnetic force), and two masses (the gravitational force) require remarkably similar equations. But, while electricity and magnetism are directly related (that’s why it’s called electromagnetism), gravity is its own fundamental force. Yet they all depend (inversely) on the square of the distance between the two objects creating the force, so they’re all said to obey some form of the inverse square law.

Gravitational Force (Fg)

The force exerted by two masses on one another is:

F_g = G \frac{m_1 m_2}{d^2}

where:

  • G is the gravitational constant (6.67300 × 10-11 m3 kg-1 s-2
  • m1 and m2 are the masses of the two objects attracting one another.
  • d is the distance between the two objects.

Electrical Force (Fe)

The force exerted by two electrically charged objects on one another (like a proton and an electron), is:

F_e = K \frac{q_1 q_2}{d^2}

where:

  • K is the electrical constant, sometimes called Coulumn’s constant (8.9876 × 109 N m2 C-2
  • q1 and q2 are the sizes of the charges (in Coulumbs) of the two objects attracting one another.
  • d is the distance between the two objects.

Magnetic Force (Fm)

The force exerted by two magnets on one another, is:

F_m = \mu \frac{p_1 p_2}{d^2}

where:

  • μ is a constant, (a little simplified)
  • p1 and p2 are strengths of the magnetic poles of the two objects attracting one another.
  • d is the distance between the two objects.

The magnetic force is a little more difficult to give a single equation for, because you need to factor in the shape of the magnets.

Inverse Square Laws

In addition to gravity, electric, and magnetic forces, light (which is electromagnetic radiation) and sound also obey inverse square laws.

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