Coulomb’s Law states that the electrical force *F*_{e} between two stationary point charges *Q*_{1} and *Q*_{2} separated by distance *d* is given by the formula

Doesn’t it look strikingly similar to ? The point masses *M*_{1} *M*_{2} are replaced by point charges *Q*_{1} *Q*_{2}. The gravitational constant is replaced by the Coulomb’s constant . Just like Newton’s law of gravitation, Coulomb’s law also obeys the inverse-square law. Furthermore, it is also a manifestation of N3L. No wonder people joke that Coulomb copied Newton’s homework.

The one major difference between gravitation and electricity is that while there is only one type of mass, there are two types of charges: positive and negative. While gravitational forces are always attractive, electric forces can be attractive (between two unlike charges) or repulsive (between two like charges).

To include the sign or not?

One thing to note. The formula is usually used to calculate the magnitude of the force only. There is no point including the signs of the charges when applying this formula. It is better and easier to figure out the direction of the forces (whether they are leftward, rightward, upward, downward etc) from the context (rather than from the formula).

Example

*Q*_{A}, *Q*_{B} and *Q*_{C} are point charges of +2.1 pC, −2.1 pC and −2.1 pC, bound at the vertices of an equilateral triangle of side 3.0 um as shown in the diagram below. Calculate the force experienced by *Q*_{C}.

Solution

The electric force exerted by *Q*_{A} on *Q*_{C},

The electric force exerted by *Q*_{B} on *Q*_{C},

Note that *Q*_{C} is attracted towards *Q*_{A}, but repelled away from *Q*_{B}. *F*_{A} and *F*_{B} are thus in the directions shown in the diagram. The resultant electric force acting of *Q*_{C} is thus given by the vector summation of *F*_{A} and *F*_{B}. By inspection, the vector summation triangle is an equilateral triangle. So *F*_{R} turns out to be a leftward force of 4.405 mN.

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**Video Explanation**

Coulomb’s Copycat Law

**Applets**

Electric Field of Dreams (PhET)

**Concept Test**

2201

**Interesting**

Electric vs Gravitation

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