# Electric field of an infinite line charge and a point charge

• amilkovi
In summary, we are given an infinite line charge with linear charge density of 2.0 microC/m along the y-axis and a point charge of 8.0 microC located at (-1.0m, 2.0m). We are asked to find the electric field at (1.0m, 2.0m) and the force on a charge of -2.0 microC at the same point. For part (a), we need to add the electric field of both the line and point charge at the given point. For part (b), we only need to consider the forces due to the fields of the other charges, not taking into account the field due to itself.
amilkovi
Electric field of an infinite line charge and a point charge!

## Homework Statement

An infinite line charge with linear charge density $$\lambda$$=2.0$$\mu$$C/m lies along the y-axis. A point charge of 8.0 $$\mu$$C is locate at (x,y)=(-1.0m, 2.0m). Find (a) the electric field at (x,y)=(1.0m, 2.0m) (b) Find the force on a charge of -2.0$$\mu$$C placed at (x,y)=(1.0m, 2.0m).

I would love if someone could point me into the right direction here!

## The Attempt at a Solution

I believe I'm gona have to add the electric field of both the line and the point charge at the point (1.0m, 2.0m) for part (a)? Then for part (b) do the same except apply the negative charge at the same point and subtract its electric field?

amilkovi said:
I believe I'm gona have to add the electric field of both the line and the point charge at the point (1.0m, 2.0m) for part (a)?
Yes.
Then for part (b) do the same except apply the negative charge at the same point and subtract its electric field?
No. The negative charge feels a force due to the fields of the other charges. You don't need to take into account the field due to itself.

## 1. What is the formula for calculating the electric field of an infinite line charge?

The formula for calculating the electric field of an infinite line charge is E = λ/2πε₀r, where λ is the charge density, π is the constant pi, ε₀ is the permittivity of free space, and r is the distance from the line charge.

## 2. How does the electric field of an infinite line charge compare to that of a point charge?

The electric field of an infinite line charge is constant and points radially away from the line, while the electric field of a point charge decreases as the distance from the charge increases. Additionally, the electric field of an infinite line charge is independent of the distance from the line, while the electric field of a point charge follows an inverse square law.

## 3. How does the direction of the electric field change for a point charge compared to an infinite line charge?

The direction of the electric field for a point charge is always radial, meaning it points directly away or towards the charge. However, for an infinite line charge, the direction of the electric field is perpendicular to the line at any given point.

## 4. What is the significance of the constant pi (π) in the formula for the electric field of an infinite line charge?

The constant pi in the formula represents the ratio of a circle's circumference to its diameter. In this context, it is used to calculate the electric field at a specific distance from the line charge, taking into account the circular shape of the field around the line.

## 5. Can the electric field of an infinite line charge be negative?

Yes, the electric field of an infinite line charge can be negative. This would indicate that the field is pointing towards the line charge, rather than away from it. The direction of the field depends on the sign of the charge density, with a positive charge density resulting in a field pointing away from the line, and a negative charge density resulting in a field pointing towards the line.

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