Question

A straight, nonconducting plastic wire 9.50cm{\rm cm}long carries a charge density of 125nC/m distributed uniformly along its length. It is lying on a horizontal tabletop. Find the magnitude and direction of the electric field this wire produces at a point 5.50student submitted image, transcription available belowdirectly above its midpoint.

Answer 1

The magnitude and direction of the electric field produced by the nonconducting plastic wire at a point directly above its midpoint can be calculated using the formula: E = (k * ρ * L) / (4π * r). The magnitude of the electric field is 1.36 N/C and its direction is pointing directly downwards since the wire has a negative charge density.

Step-by-step explanation:

The magnitude and direction of the electric field produced by the nonconducting plastic wire at a point directly above its midpoint can be calculated using the formula:

E = (k * ρ * L) / (4π * r)

Where:

1. E is the electric field
2. k is the Coulomb constant, approximately equal to 9 x 10^9 N m^2/C^2
3. ρ is the charge density of the wire
4. L is the length of the wire
5. r is the distance between the point and the midpoint of the wire

Substituting the given values into the formula:

E = (9 x 10^9 N m^2/C^2 * 125 x 10^(-9) C/m * 0.095 m) / (4π * 0.055 m)

Simplifying the expression:

E = 1.36 N/C

The magnitude of the electric field is 1.36 N/C and its direction is pointing directly downwards since the wire has a negative charge density.