Y-component of Electrostatic Force

[vg19]

Homework Statement

Calculate the X, Y, and magnitude force between the two charges. Compare to the computer simulation results.

Homework Equations

Do not forget that this is a 2-D problem. Use the 2-D Coulomb’s law for line charges.

The Attempt at a Solution

Basically we used a software called MAXWELL to plot 2 charges, 1 source and 1 probe charge. The source had a charge of 1 x 10^-12 C and probe -1 x 10^-13 C. The source charge had a radius of 5mm, while the probe had a radius of 0.5mm and the distance between them (Centre to centre) is 10mm. Both charges lie on the x-axis.

The software gave the following results,
Fx = -1.8E-13
Fy= 3.1E-16
Fmag =1.8E-13
Angle=180


I do know how to calculate the x-component, however I am confused on the y component. If both charges lie on the x-axis, wouldn't there only be an x-component of Force? How would I go about calculating it?

Thanks

 

[TristanJ]

Tired and probably wrong...

Well, I'm very tired at the moment (late night doing EE homework!) but offhand I would say you are correct, if both charges lie on the x-axis, the y component should be zero. It is possible that the result from your computer simulation is a "virtual" zero, i.e. errors in the calculation introduced from using a finite number of bits in base 2 means that the answer is not EXACTLY zero, but is extremely close... remember that your y-component that you found is 1/1000th of the X component (approx.) You can see this in MATLAB quite often as well, when an answer of say 1E-60 is considered a 0 in many situations. Sorry if I am totally off base here!

Regards,
Tristan Jones

 

[m2003]

for your question. In this case, the y-component of the electrostatic force refers to the force acting in the y-direction, even though both charges may lie on the x-axis. This is because the charges still have a separation in the y-direction, and thus there will be a force acting in that direction. To calculate the y-component of the force, you can use the 2-D Coulomb's law for line charges, which takes into account the separation in both the x and y directions. You can then compare your calculated result to the computer simulation results to check for accuracy.