# Finding the magnitude of the electrostatic force from a thin rod

• nuagerose
In summary: Please consult a calculus textbook for more information.In summary, when dealing with a charged thin rod, you need to integrate to find the electrostatic force acting on an electron.

## 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 [Broken]

## Homework Equations

F = $\frac{kQ}{d^{2}}$

## 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-$\frac{L}{2}$ as the d in the above equation.

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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.

Tanya Sharma said:
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$_{1}$*q$_{2}$)/r$^{2}$

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.

nuagerose said:
F = (k*q$_{1}$*q$_{2}$)/r$^{2}$

Hope this is right.

Right

nuagerose said:
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.

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.

## 1. What is the formula for calculating the magnitude of the electrostatic force from a thin rod?

The formula for calculating the magnitude of the electrostatic force from a thin rod is F = (k * Q * q) / r2, where k is the Coulomb's constant (9 x 109 N * m2 / C2), Q is the charge of the rod, q is the point charge, and r is the distance between the rod and the point charge.

## 2. What is a thin rod in the context of electrostatics?

In electrostatics, a thin rod is a one-dimensional object with a negligible thickness and a uniform distribution of charge along its length. This means that the charge is evenly spread out along the entire length of the rod.

## 3. How do I determine the direction of the electrostatic force from a thin rod?

The direction of the electrostatic force from a thin rod can be determined using the principle of superposition. This states that the total force on a point charge due to multiple point charges can be found by adding up all the individual forces acting on that point charge. The direction of the total force will be in the same direction as the vector sum of the individual forces.

## 4. Can the magnitude of the electrostatic force from a thin rod be negative?

Yes, the magnitude of the electrostatic force from a thin rod can be negative. This indicates that the force is acting in the opposite direction of the force calculated using the formula. This can occur if the point charge and the rod have opposite charges, resulting in an attractive force instead of a repulsive force.

## 5. What factors can affect the magnitude of the electrostatic force from a thin rod?

The magnitude of the electrostatic force from a thin rod can be affected by the amount of charge on the rod (Q), the amount of charge on the point charge (q), and the distance between the rod and the point charge (r). The force will increase if any of these factors increase, and decrease if any of these factors decrease.