How can I calculate the electric field and force between two charged rods?

In summary, the electric field and the magnitude of the force exerted by the left rod on the right one are calculated.
  • #1
Nasserz
4
0
[SOLVED] Electric field and force ...

Homework Statement


We have 2 identical thin rods , each has a length of 2a and carry a charge of +Q , uniformly distributed along their lengths , and both lie on the horizontal X-axis , and the distance between their centers is "b" ...
I need to calculate the electric field and the magnitude of the force exerted by the left rod on the right one.


Homework Equations


I know that F=Q*E
and the electric field done by a charged rod on a point in its axis is E= K*Q/d(d+L) where L is the length of the rod , and d is the distance between the rod and the point.


The Attempt at a Solution


Well I didn't know how to start :S , no need for a full solution , I just need a push and tell me how to start to solve it .. thanks.
 
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  • #2
You have to integrate along the length of the right rod.

If [itex]\lambda[/itex] is the linear charge density of the right rod, then find the force due to left rod on an element of length dx on the right rod which is at a distance of x from the left rod. Now integrate, putting the proper limits of x, that is, the values of x on the left and right extremities of the rod on the right respectively.
 
  • #3
can someone explain a litle bit more .. didn't really understand ... my english isn't that good
 
  • #4
Nasserz said:

Homework Equations


I know that F=Q*E
and the electric field done by a charged rod on a point in its axis is E= K*Q/d(d+L) where L is the length of the rod , and d is the distance between the rod and the point.


The Attempt at a Solution


Well I didn't know how to start :S , no need for a full solution , I just need a push and tell me how to start to solve it .. thanks.

So you don’t need a push, but a slightly bigger shove. Here goes!

Draw a diagram first of the two rods. Take a small length dx on the right rod, at a distance x from the right tip of the left rod. This dx length has got a charge of dq = [itex]
\lambda[/itex]dx.

What is the field at this point due to the charge of the left rod? This is at a distance of x from the right end of the left rod. Apply the formula you have written. (I have not checked it, but looks all right.) The field should be then KQ/[x(x+2a)].

So the force on this dq on the right rod should be given by:

dF = Field*Charge = KQdq/[x(x+a)] = K[itex]\lambda[/itex]dx/[x(x+a)] => the total force F should be given by:

[tex]F = \int^{b}_{b-2a}\frac{KQ\lambda dx}{x(x+2a)}[/tex].
 
Last edited:
  • #5
thanks mate , that's very helpful ... :)
 
  • #6
I continued the integration .. and I got as final answer : F = (KQ^2/4a^2)ln(b^2/b^2 - 4a^2)
I think it is right , can you confirm this ?
thanks a lot mate , I really appreciate your help ^_^ , you are the best.
 
  • #7
Nasserz said:
I continued the integration .. and I got as final answer : F = (KQ^2/4a^2)ln(b^2/b^2 - 4a^2)

Bracket is missing: (KQ^2/4a^2)ln(b^2/(b^2 - 4a^2)).
 

1. What is an electric field?

An electric field is a physical quantity that describes the influence that a charged particle exerts on other charged particles in its vicinity. It is a vector quantity, meaning it has both magnitude and direction.

2. How is an electric field created?

An electric field is created by a charged object, such as an electron or a proton. The charge of the object causes a disturbance in the space around it, which creates an electric field.

3. How is the strength of an electric field measured?

The strength of an electric field is measured in units of force per unit charge, or newtons per coulomb. This is also known as the electric field intensity.

4. What is the relationship between electric field and force?

The force exerted on a charged particle in an electric field is directly proportional to the electric field strength and the charge of the particle. This relationship is described by the equation F = qE, where F is the force, q is the charge, and E is the electric field strength.

5. How does distance affect the strength of an electric field?

The strength of an electric field decreases as the distance from the source of the field increases. This relationship follows the inverse square law, meaning that the electric field strength is inversely proportional to the square of the distance from the source.

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