Finding the magnitude of the electrostatic force from a thin rod

[nuagerose]

Homework Statement

The figure shows a uniformly charged thin rod of length L that has total charge Q. Find an expression for the magnitude of the electrostatic force acting on an electron positioned on the axis of the rod at a distance d from the midpoint of the rod.

http://ezto.mhecloud.mcgraw-hill.com/13252699451980596522.tp4?REQUEST=SHOWmedia&media=c21q56a.png

Homework Equations

F = [itex]\frac{kQ}{d^{2}}[/itex]

The Attempt at a Solution

I know how to find the force from a point charge using the equation above, but I am not sure how to set up this problem because it is a charged thin rod. I was thinking I could divide Q by L as the charge in the above question and d-[itex]\frac{L}{2}[/itex] as the d in the above equation.

 

[Tanya Sharma]

Can you tell what is the formula for the force between two point charges q1 and q2 at a distance d from each other ? The formula you have written doesn't make much sense.

 

[nuagerose]

Can you tell what is the formula for the force between two point charges q1 and q2 at a distance d from each other ? The formula you have written doesn't make much sense.

F = (k*q[itex]_{1}[/itex]*q[itex]_{2}[/itex])/r[itex]^{2}[/itex]

Hope this is right. I suppose q1 would be the charge of the thin rod and q2 would be the charge of the point, which is e.

 

[Tanya Sharma]

F = (k*q[itex]_{1}[/itex]*q[itex]_{2}[/itex])/r[itex]^{2}[/itex]

Hope this is right.

Right

I suppose q1 would be the charge of the thin rod and q2 would be the charge of the point, which is e.

No.Coulomb's law applies only to point charges.You cannot apply this directly when a continuous object like a rod is present.We will have to consider rod as composed of infinitely many point charges.

Are you familiar with calculus ?You will need integration whenever a continuous charged body is present.

 

[Nickie]

I would approach this problem by first considering the concept of electric fields. The electric field produced by a thin rod of length L and charge Q can be calculated using the equation E = kQ/L, where k is the Coulomb's constant. This electric field can then be used to calculate the force on an electron placed at a distance d from the midpoint of the rod.

To find the magnitude of the electrostatic force, we can use the equation F = qE, where q is the charge of the electron. In this case, the charge of the electron is negative, so the force will be directed towards the rod.

Therefore, the magnitude of the electrostatic force on the electron can be calculated as F = q(kQ/L) = (1.6x10^-19 C)(9x10^9 Nm^2/C^2)(Q/L). This can be simplified to F = (1.44x10^-9 N)(Q/L).

One important thing to note is that the distance d in the equation provided in the problem is the distance from the midpoint of the rod, not the distance from the electron to the rod. So, we can use the Pythagorean theorem to find the actual distance from the electron to the rod, which would be d' = √(d^2 + L^2/4).

Therefore, the final expression for the magnitude of the electrostatic force on the electron can be written as F = (1.44x10^-9 N)(Q/L)(d'/(d^2 + L^2/4)). This takes into account the fact that the electric field and force decrease as the distance from the midpoint of the rod increases.

In conclusion, as a scientist, I would approach this problem by first understanding the concept of electric fields and using that to calculate the force on the electron. I would also carefully consider the given information and make sure to use the correct distances in the equations.