Question

Two parallel, uniformly charged, infinitely long wires carry opposite charges with a linear charge density ? = 2.37 ?C/m and are 5.47 cm apart. What is the magnitude of the electric field at a point midway between them and 51.9 cm above the plane containing the two wires?

Answer 1

Refer the figure below.

We have AB = 5.47 cm
OC = 51.9 cm
Wires are bold darkened lines.

We need to find field at point C.

Field at C is due to wires. Let they be E₁ and E₂.
Electric field at a distance z from infinitely long wire =

Here Z is same for both = sqrt(51.9² + 2.73²)
= 51.97 cm

So, E₁ = E₂ =

= 0.0806 * 10^-15 N/C

Now net field due to E₁ and E₂ would be in upwards.
Angle BCO from figure
= arctan(2.57/51.9)
= 0.29^o

Hence the fields due to wires point at 0.29^o wrt vertical.

So, net field = 2 * cos0.29^o* E₁
= 0.16 * 10^-15 N/C
= 1.6 * 10^-16 N/C

Ans : 1.6 * 10^-16 N/C