Question

A very long copper rod has a radius of 1 cm. the electric field at a distance 5.75 cm from the center axis of the rod has a magnitude of 4.6 n/c and is directed away from the rod.

a) What is the charge per unit length, in coulombs per meter, on the copper rod? b) Suppose the rod passes through a Gaussian surface which is a cube with an edge length L=5.5 cm as, shown. The rod is perpendicular to the faces through which it passes, and it extends well beyond the edges of the sketch. What is the electric flux, in newton squared meters per coulomb, through the cube?

Answer 1

a) The charge per unit length on the copper rod is 7.88x10^-20 C/m. b) The electric flux through the cube is 0.01393 N.m^2/C.

Step-by-step explanation:

a) To find the charge per unit length on the copper rod, we can use the formula:

E = λ/2ε0

Where E is the electric field, λ is the charge per unit length, and ε0 is the permittivity of free space. Rearranging the formula, we have:

λ = 2ε0E

Substituting the given values, λ = 2(8.85x10-12 C2/N.m2)(4.6x10-9 N/C) = 7.88x10-20 C/m

b) To find the electric flux through the cube, we can use Gauss's law:

Φ = E*A

Where Φ is the electric flux, E is the electric field, and A is the area of the Gaussian surface. The area of each face of the cube is L2 = (0.055 m)2 = 0.003025 m2. Since the rod is perpendicular to the faces, the electric field is constant and equal to 4.6 N/C, so the electric flux is Φ = 4.6 N/C * 0.003025 m2 = 0.01393 N.m2/C.