Uniform Charge, Electric Field

[Digdug12]

Homework Statement

A very long uniform line of charge has charge per unit length 5.38 micro coulombs /m and lies along the x-axis. A second long uniform line of charge has charge per unit length -3.66 micro coulombs /m and is parallel to the x-axis at y = 0.400m. What is the net magnitude of the electric field at the point y = 0.200m? Give your answer in N/C in scientific notation to three significant digits.

Homework Equations

E=1/2pi(Epsilon)*[Uniform Charge length/R^2]

The Attempt at a Solution

I tried summing the two electric fields by using the above equation for each uniform charge and adding them together, however the answer is wrong. I also used 1/4pi(epsilon) but it was still wrong, what am i missing?

 

[LowlyPion]

Homework Statement

A very long uniform line of charge has charge per unit length 5.38 micro coulombs /m and lies along the x-axis. A second long uniform line of charge has charge per unit length -3.66 micro coulombs /m and is parallel to the x-axis at y = 0.400m. What is the net magnitude of the electric field at the point y = 0.200m? Give your answer in N/C in scientific notation to three significant digits.

Homework Equations

E=1/2pi(Epsilon)*[Uniform Charge length/R^2]

The Attempt at a Solution

I tried summing the two electric fields by using the above equation for each uniform charge and adding them together, however the answer is wrong. I also used 1/4pi(epsilon) but it was still wrong, what am i missing?

Keep i mind that the E-field is a vector field.

Add like a vector instead of just summing, because direction matters.

In this case since they are opposite signs, and your point is in the middle, your answer should be ...

|E| = |E1| + |E2|

 

[nlightner]

When calculating the electric field from a uniform line of charge, you need to take into account the distance from the point to the line of charge. The equation you have used, E=1/2pi(Epsilon)*[Uniform Charge length/R^2], assumes that the point is at a distance R from the line of charge. However, in this problem, the point is at a distance of 0.2m from the line of charge, not R.

To correctly calculate the electric field at the point y=0.2m, you can use the superposition principle, which states that the net electric field at a point due to multiple charges is the vector sum of the individual electric fields at that point. In this case, you have two charges with different directions and magnitudes, so you need to add them as vectors.

The electric field from the first line of charge can be calculated using the equation E=1/2pi(Epsilon)*[Uniform Charge length/R], where R is the distance from the point to the line of charge. In this case, R=0.2m. The electric field from the second line of charge can be calculated using the same equation, but with a negative sign since the charge is in the opposite direction.

Once you have calculated the electric fields from both lines of charge, you can add them as vectors to find the net electric field at the point y=0.2m. The magnitude of the net electric field can then be expressed in Newtons per Coulomb (N/C) and rounded to three significant digits using scientific notation.

I hope this helps you find the correct solution. Remember to always consider the distance from the point to the line of charge when calculating the electric field from a uniform line of charge.