Magnitude and Direction of a charge interaction

[themonk]

Homework Statement

What is the direction of the force [tex]\vec{F}[/tex] on the -10 nC charge in the figure? Give your answer as an angle measured cw from the +x-axis. Problem 26.39 in Physics for Scientists and Engineers Second Edition by Knight
Magnitude of the force is 4.3E-3 N

Homework Equations

As far as I know, this is the only relevant equations:

[tex]\vec{F}[/tex]=[tex]k*q_{1}*q_{2}/d^{2}[/tex]

The Attempt at a Solution

I already found the magnitude as listed above. But I need to find [tex]\theta[/tex] in the clockwise direction.

The force of A (being the -5 nC charge) I figured was direction -4.3E-4 [tex]\hat{j}[/tex] and -1.28E-3 [tex]\hat{i}[/tex] and the other charge had a force of -4.5E-3 I double checked with an answer from someone else (MasteringPhysics also said it was correct). I figured I would use a trigonometric function for the final part, ie the angle measured in the clockwise direction. In lab we used tangent, but was confused as to why (tangent is opposite over adjacent):

tan([tex]\theta[/tex])=4.07E-3/1.28E-3 ==> [tex]\theta[/tex]=tan[tex]^{-1}[/tex](3.179)

which is 72.54 degrees. I added 180 to it to get 252.54, but apparently that is not correct (I don't completely understand the cw and ccw part).

Is there any line of thought that I should proceed with?

(sorry about my English)

 

[ehild]

Show the coordinate axes and the forces in your figure, please.

ehild

 

[themonk]

I can't edit the problem, but the x-axis ([tex]\hat{i}[/tex]) is left-right and the y-axis ([tex]\hat{j}[/tex]) would be up-down, if I am not mistaken. The origin would then be at the -10nC.

 

[ehild]

In this case the force on the -10 nC charge from the -5 nC one has only y component, and that form the 15 nC charge has both x and y components. Check your calculation and text.

ehild

 

[rwisz]

I would approach this problem by first analyzing the given information and understanding the physical scenario. The problem involves two charges, one being -10 nC and the other unknown, with a given magnitude of force and a desired angle of direction.

Next, I would apply the relevant equation for Coulomb's law to calculate the force between the two charges. From the given magnitude of the force, we can determine the value of the product of the two charges and the distance between them.

Once we have the force vector, we can use vector addition to determine the direction of the force on the -10 nC charge. This can be done by breaking the force vector into its horizontal and vertical components and using trigonometric functions to determine the angle.

In this case, the force vector is directed towards the negative x-axis, so the angle measured clockwise from the positive x-axis would be 180 degrees. However, if we consider the direction of the force on the -10 nC charge, we can see that it is directed towards the -x direction (opposite of the +x direction). Therefore, the angle measured clockwise from the +x-axis would be 0 degrees.

In conclusion, the direction of the force on the -10 nC charge is towards the -x direction, with an angle of 0 degrees measured clockwise from the +x-axis.