A very long uniform line of charge has charge per unit length 3.70 µC/m and lies along the x-axis. A second long uniform line of charge has charge -2.20 µC/m per unit length and is parallel to the x-axis at y = 0.400 m. What is the net electric field (magnitude and direction) at the following points on the y-axis?
a) y=0.200m
b)y=0.600m
For A I got 5.31*10^5 and it was correct but for B I got 8.69*10^5 and its wrong.
How do you do part B?
To calculate the net electric field at a point on the y-axis due to two parallel lines of charge, we need to consider the electric field contribution from each line and then find the vector sum of these two contributions.
Let's start with point B, where y = 0.600 m.
1. Electric field due to the first line of charge:
The electric field at point B due to the first line of charge parallel to the x-axis can be determined by using Coulomb's Law. For a uniformly charged line, the electric field at a perpendicular distance (r) from the line is given by the equation:
E1 = (k * λ1) / r,
where E1 is the electric field, k is the electrostatic constant (9 * 10^9 N m^2/C^2), λ1 is the charge density (charge per unit length) of the first line, and r is the distance between the point and the line.
Substituting the values into the equation, we have:
E1 = (9 * 10^9 N m^2/C^2) * (3.70 µC/m) / y,
where y is the distance between the point and the first line.
2. Electric field due to the second line of charge:
Similarly, we can calculate the electric field at point B due to the second line of charge. Since the charge density for the second line is given as -2.20 µC/m, the electric field for this line would have the opposite direction.
E2 = -(9 * 10^9 N m^2/C^2) * (2.20 µC/m) / y,
where y is the distance between the point and the second line.
3. Net electric field at point B:
To find the net electric field, we need to add the electric field contributions from both lines.
E_net = E1 + E2.
Substitute the previously calculated values of E1, E2, and y to get the net electric field at point B.
It's important to note that since the second line of charge has a negative charge density, the electric field contribution from that line will have the opposite direction compared to the first line. This is why the magnitude of the electric field at point B differs from point A.