Question

Three infinitely long lines of charge with uniform line charge densities, τ1​=5nC/m,τ2​=−5nC/m, and τ3​=5nC/m, are parallel to the z axis. If they pass through the respective points (0,−b),(0,0), and (0,b) in the x−y plane, find the electric field at (a,0,0). Evaluate your result for a=2 cm and b=1 cm. Assume that the surrounding medium is air. Show and explain all steps. Answer:

Answer 1

To find the electric field at a point (a,0,0) due to three infinite lines of charge, use the principle of superposition. Calculate the electric field due to each line charge separately using the formula E = (1/4πε₀) * (λ / r), where λ is the line charge density and r is the distance between the point and the line of charge. Add up the electric field vectors of each line charge to find the total electric field at the given point.

Step-by-step explanation:

To find the electric field at the point (a,0,0) due to the three infinite lines of charge, we can use the principle of superposition. The electric field due to each line of charge can be calculated separately and then added vectorially. Let's denote the line charges as τ1, τ2, and τ3 and their respective points as A, B, and C.

First, let's calculate the electric field at point A, which is on the x-axis and has coordinates (a,0,0). The electric field at point A due to τ1 is given by:
E1 = (1/4πε₀) * (τ1 / r1), where r1 is the distance between point A and the line of charge τ1. Similarly, the electric field at point A due to τ2 and τ3 can be calculated using the same formula. After finding the electric field vectors for each line of charge, add them up vectorially to find the total electric field at point A.

Using the given values of τ1, τ2, τ3, a=2 cm, and b=1 cm, substitute the values into the formulas and calculate the electric fields due to each line charge. Then add them up to find the total electric field at point (a,0,0).