Question

A very long straight wire has charge per unit length 1.53×10⁻¹⁰ C/m .

At what distance from the wire is the magnitude of the electric field equal to 2.60 N/C ?[ Use 8.85×10⁻¹² C²/(N×m²) for the permittivity of free space, and use π=3.14159.]

Answer 1

The distance from a long straight wire with a charge per unit length of 1.53×10⁻¹⁰ C/m at which the electric field is 2.60 N/C is approximately 0.358 meters.

Step-by-step explanation:

To find the distance from the wire at which the magnitude of the electric field is equal to 2.60 N/C, given the charge per unit length (λ = 1.53×10⁻¹⁰ C/m), we use the formula for the electric field (E) around a long straight wire:

E = (λ / (2πε⁰r))

where ε⁰ is the permittivity of free space (8.85×10⁻¹² C²/(N·m²)) and r is the distance from the wire. Rearranging to find r, we get:

r = λ / (2πε⁰E)

Substitute the given values:

r = (1.53×10⁻¹⁰ C/m) / (2·3.14159·8.85×10⁻¹² C²/(N·m²)·2.60 N/C)

After calculating, we find:

r ≈ 0.358 meters

So, the distance from the wire where the electric field magnitude is equal to 2.60 N/C is approximately 0.358 meters.