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 E_{1} and
E_{2}.

Electric field at a distance z from infinitely long wire =

Here Z is same for both = sqrt(51.9^{2} +
2.73^{2})

= 51.97 cm

So, E_{1} = E_{2} =

= 0.0806 * 10^{-15} N/C

Now net field due to E_{1} and E_{2} 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}* E_{1}

= 0.16 * 10^{-15} N/C

= 1.6 * 10^{-16} N/C

**Ans : 1.6 * 10 ^{-16} N/C**

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