A charge of #-2 C# is at #(4, 7)# and a charge of #-1 C# is at #( 1 , -6 )#. If both coordinates are in meters, what is the force between the charges?

1 Answer
David B.
Mar 2, 2016

Each charge experiences a repulsive force of #F= 1.01xx10^8N#

Explanation:

Let's start by creating a diagram of the information that we know:

enter image source here

We know from Coulomb's Law that the force between charges depends on the size and sign of the charges, and on the distance between them:

#F = k_e |q_1 q_2|/r^2#

Where #q_1# and #q_2# are the two charges, #k_e# is Coulomb's constant #(k_e = 8.99xx10^9 N m^2 C^(−2))#, and #r# is the distance between the charges. We see that we need to calculate #r^2# which can be gotten by using Pythagoras's Theorem on the right triangle shown in the diagram:

#r^2=Delta x^2 +Delta y^2 = (3m)^2+(13m)^2 = 178m^2#

We can now get the force:

#F= 8.99xx10^9 N m^2 C^(−2) * |(-2C)*(-1C)|/(178m^2)=1.01xx10^8N#

Each charge experiences this force which is repulsive, since they have the same sign of charge.

Advanced:

The constant #k_e# can be expressed in terms of the SI constant, the permittivity of free space #epsilon_o#, as:

#k_e=1/(4 pi epsilon_o)#

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