Coulombs force law in a three dimensional coordinate system problem

[SirPlus]

Two point charges of Q1 = +37 nC and Q2 = +70 nC are located at points (1,3,0) m and (0,0,2) m, respectively.

Q : Calculate the force exerted on Q2 by Q1.

Attempt : I applied phythagoras theorem to find the distance between Q1 and Q2, I then applied coulombs force law equation directly given r,Q1,Q2, however I am puzzled to how I could find the direction of the force and how possible i could solve the problem in vector notation ..

 

[ehild]

Hi SirPlus, welcome to PF.

What does Coulomb's law say about the direction of the force between two charges?

ehild

 

[SirPlus]

Nothing much, it simply tells us about the magnitude of the electrostatic force exerted on charge by the other and that this force is directly proportional to the product of charges and inversly proportional to the square of the distance between the centre of the charges - i am however intersted in the orientation of the coulombs force in a 3d space like a coordinate system, after all force is a vector quantity...

 

[SirPlus]

Thanks for the invitation dude

 

[vanhees71]

That's right! Forces are vectors. For the Coulomb Law it's
$$\vec{F}=\frac{q_1 q_2 (\vec{r}_1-\vec{r}_2)}{|\vec{r}_1-\vec{r}_2|^3}.$$
That's the force acting on a charge $q_1$ at position $\vec{r}_1$ due to a charge $q_2$ at position $\vec{r}_2$ (in Heaviside-Lorentz units).

 

[ehild]

Nothing much, it simply tells us about the magnitude of the electrostatic force exerted on charge by the other and that this force is directly proportional to the product of charges and inversly proportional to the square of the distance between the centre of the charges - i am however intersted in the orientation of the coulombs force in a 3d space like a coordinate system, after all force is a vector quantity...

See: http://faculty.wwu.edu/vawter/PhysicsNet/Topics/ElectricForce/CoulombLaw.html

The Coulomb force is a vector, parallel with the line connecting the charges. The force q1 exerts on q2 points from q1 to q2, parallel with the difference of the position vectors Δr=r2-r1, if both charges have the same sign, otherwise it is in the opposite direction.
The exact, vectorial formula of the Coulomb force is what vanhees71 wrote. You need to multiply the magnitude of the Coulomb force with the unit vector parallel to Δr.

ehild

 

[SirPlus]

Sure, but doesn't tell me anything about the orientation of the force in a three dimensional space?

 

[ehild]

Sure, but doesn't tell me anything about the orientation of the force in a three dimensional space?

It does. The force is parallel to the difference of the position vectors. The position vectors r1 and r2 are given. What is their difference?

ehild

 

[SirPlus]

Thanks so we use vector notation, thanks pretty clear now ...