A charge of -2 C is at (-5 , 1 ) and a charge of -3 C is at (0 ,4) . If both coordinates are in meters, what is the force between the charges?

1 Answer
May 20, 2017

Magnitude of vecF : 4.46 xx 10^10 N

Direction of vecF_(1"on"2) : 31.0^o

Direction of vecF_(2"on"1) : 211.0^o

Explanation:

We can solve this equation by using Coulomb's law, which relates the magnitude of the electric force between two point charges, and in equation form is

F = 1/(4piepsilon_0)(|q_1q_2|)/(r^2)

The quantity 1/(4piepsilon_0) is a proportionality constant, and can sometimes be simply called k, and has a value of 1/(4pi(8.854 xx 10^-12(C^2)/(N*m^2)))

= 8.988 xx 10^9(N*m^2)/(C^2)

The variables q_1 and q_2 are, in no particular order, the magnitude of the electric charges of the two point charges, which are -2C and -3C. The variable r is the distance between the two point charges, which is

|sqrt((-5m)^2 + (1m)^2) - sqrt((0m)^2 + (4m)^2)| = 1.10m

Now that we have all the variables needed, the magnitude of the electric force between the two points is

F = 8.988 xx 10^9(N*m^2)/(C^2)((|(-2C)(-3C)|)/((1.10m)^2))

= color(blue)(4.46 xx 10^10 N

Since both point charges are negative, the force is repulsive, and is the magnitude of the force the particles act upon each other.

If you want the direction of the force, which completes the vectoral description of the force of repulsion, we can use the fact that the force of object 1 acting on 2 is equal to the negative of the force of object 2 acting on 1.

If we let the point with charge -2C with coordinates (-5,1) be color(orange)1, and the point with charge -3C with coordinates (0,4) be color(red)2 (for convenience), the direction of vec F_(color(orange)1"on"color(red)2) is

arctan((y_2-y_1)/(x_2-x_1)) = arctan((4m-1m)/(0m--5m)) = color(green)(31.0 ^o

The direction of vec F_(2"on"1) is simply the direction opposite to this in a circle:

180.0^o + color(green)(31.0^o) = color(purple)(211.0^o