Electric Field due to Infinite Line of Charge

a) What is the total charge enclosed by the Gaussian cylinder?

No multiple choice available.

b) What is the electric flux through the cylinder due to the infinite line of charge?

No multiple choice available.

c) Calculate the electric field at a point 3 m away from the infinite line of charge.

No multiple choice available.

Answer:

The total charge enclosed by the Gaussian cylinder is 112.5μC. The electric flux through the cylinder due to the infinite line of charge is 1.27 x 10^13 N·m^2/C. The electric field at a point 3 m away from the infinite line of charge is 1.34 x 10^9 N/C.

To calculate the total charge enclosed by the Gaussian cylinder, we need to multiply the linear charge density by the length of the cylinder. The linear charge density is given as 75μC/m, and the length of the cylinder is given as 1.5 m. Therefore, the total charge enclosed is:

Q = (linear charge density) x (length of the cylinder)

Q = 75μC/m x 1.5 m

Q = 112.5μC

To calculate the electric flux through the cylinder due to the infinite line of charge, we can use Gauss's Law. The electric flux is equal to the total charge enclosed divided by the permittivity of free space. The permittivity of free space, ε₀, is a constant equal to 8.85 x 10^-12 C^2/(N·m^2).

Electric flux = (total charge enclosed) / (permittivity of free space)

Electric flux = 112.5μC / (8.85 x 10^-12 C^2/(N·m^2))

Electric flux = 1.27 x 10^13 N·m^2/C

To calculate the electric field at a point 3 m away from the infinite line of charge, we can use the formula E = (λ / 2πε₀r), where λ is the linear charge density, ε₀ is the permittivity of free space, and r is the distance from the line of charge.

Electric field = (linear charge density) / (2πε₀r)

Electric field = 75μC/m / (2π x 8.85 x 10^-12 C^2/(N·m^2) x 3 m)

Electric field = 1.34 x 10^9 N/C