Deriving Electric Field in y-direction from Line Charge of Lambda=4.5 nC/m

In summary, the problem involves finding the electric field in the y direction caused by a line charge with a density of lambda=4.5 nC/m on the x-axis from x=-5cm to x=5cm. The solution involves summing the electric fields in the y direction caused by each dx along the line with a charge dq. The greatest electric field is expected to be at x=0 and then at some distance y from the line. The distance at which the electric field maximizes can be found through triangulation and vector addition of the j-components from the two integrals.
  • #1
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A line charge of liner charge density lambda=4.5 nC/m lies on the x-axis and extends from x=-5cm to x=5cm. Derive an expression for E_y.

I have started with this question and it seems that I have to sum the electric fields in the y direction caused by each dx along the line with a charge dq. I think I understand how to do the integral but I just don't know what the field in the y direction is? Thanks for any help.
 
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  • #2
Just imagine that the apparent charge, when 'felt' from test charges away from the rod convene to a equidistant point on both sides of this rod. Consider this to be the y-distance away from the x-axis (rod). Since this rod is of finite length, then you should approximate the greatest electric field to be at x=0, and then at some distance y from the bar. Now, all you have to do is find how far away from y=0 the electric field maximizes. You can simply triangulate to find this point, and then use vector addition of the j-components from the two integrals.
 

1. What is a line charge?

A line charge is an imaginary line that represents an infinite charged wire. It is used in physics to simplify calculations involving electric fields and charges.

2. How is the electric field derived from a line charge?

The electric field is derived by using Coulomb's Law, which states that the electric field at a point is equal to the force between two charges divided by the distance between them. In the case of a line charge, the electric field can be calculated by dividing the charge per unit length (lambda) by the distance from the line charge.

3. What does lambda represent in the given scenario?

In this scenario, lambda represents the charge per unit length of the line charge. It is measured in units of coulombs per meter (C/m) and indicates the amount of charge present on a one-meter section of the line charge.

4. How does the electric field vary with distance from the line charge?

The electric field varies inversely with distance from the line charge. This means that as the distance from the line charge increases, the electric field decreases. This relationship can be mathematically represented by the equation E ∝ 1/r, where E is the electric field and r is the distance from the line charge.

5. Can the direction of the electric field from a line charge change?

Yes, the direction of the electric field from a line charge can change depending on the position of the point in relation to the line charge. If the point is above or below the line charge, the electric field will be directed radially away or towards the line charge. If the point is on the same plane as the line charge, the electric field will be directed tangentially to the line charge.

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