Question

A very long uniform line of charge has charge per unit length 4.62 μC/m and lies along the x-axis. A second long uniform line of charge has charge per unit length -2.52 μC/m and is parallel to the x-axis at y1 = 0.402 m 1) What is the magnitude of the net electric field at point y2 = 0.220 m on the y-axis? 2) What is the magnitude of the net electric field at point y3 = 0.600 m on the y-axis?

Answer 1

Answer 2

To find the magnitude of the net electric field at different points along the y-axis due to the two long uniform lines of charge, we can use the principle of superposition. We'll calculate the electric fields due to each line separately and then sum them to get the net electric field.

Given data: Line 1: Charge per unit length = 4.62 μC/m Line 2: Charge per unit length = -2.52 μC/m

1. Net Electric Field at y2 = 0.220 m: To calculate the net electric field at point y2, we need to consider the electric fields due to both lines of charge.

For Line 1: The electric field at point y2 due to Line 1 can be calculated using the formula: E1 = (k * λ1) / y1

where k is Coulomb's constant (8.99 x 10^9 N m^2/C^2), λ1 is the charge per unit length of Line 1 (4.62 μC/m), and y1 is the distance of Line 1 from the point (0.402 m).

E1 = (8.99 x 10^9 N m^2/C^2 * 4.62 x 10^-6 C/m) / 0.402 m

For Line 2: The electric field at point y2 due to Line 2 can be calculated similarly: E2 = (k * λ2) / y2

where λ2 is the charge per unit length of Line 2 (-2.52 μC/m) and y2 is the distance of Line 2 from the point (0.220 m).

E2 = (8.99 x 10^9 N m^2/C^2 * -2.52 x 10^-6 C/m) / 0.220 m

The net electric field at point y2 is the sum of the electric fields due to Line 1 and Line 2: E_net = E1 + E2

2. Net Electric Field at y3 = 0.600 m: We can follow the same procedure as above to calculate the net electric field at point y3.

For Line 1: E1 = (k * λ1) / y1

For Line 2: E2 = (k * λ2) / y3

The net electric field at point y3 is the sum of the electric fields due to Line 1 and Line 2: E_net = E1 + E2

By plugging in the given values and performing the calculations, we can find the magnitudes of the net electric fields at points y2 and y3.