10. A 5 meter length of wire has a charge density of 3 x 10-3 C/m. What is the electric field strength E at an axial distance of 0.25 meters from the wire?
To find the electric field strength E at an axial distance of 0.25 meters from the wire, we can use Coulomb's Law. Coulomb's Law states that the electric field strength due to a charged wire is directly proportional to the charge density (λ) and inversely proportional to the distance (r) from the wire.
The equation for the electric field strength E (in N/C) due to a charged wire is given by:
E = λ / (2πε₀r),
where λ is the charge density in C/m, ε₀ is the permittivity of free space (constant value of 8.85 x 10^-12 C^2/Nm^2), and r is the distance from the wire in meters.
Let's plug in the given values into the equation:
λ = 3 x 10^-3 C/m (charge density),
r = 0.25 meters (distance from the wire),
ε₀ = 8.85 x 10^-12 C^2/Nm^2 (permittivity of free space).
E = (3 x 10^-3 C/m) / (2π(8.85 x 10^-12 C^2/Nm^2)(0.25 meters)).
Simplifying this equation will give us the electric field strength E at a distance of 0.25 meters from the wire.