A long, straight metal rod has a radius of 4.50 cm and a charge per unit length of 30.0 nC/m. Find the electric field at the following distances from the axis of the rod, where distances are measured perpendicular to the rod.

a)3.00 cm
b)13.5 cm
c)120 cm

To find the electric field at a distance from the axis of the rod, we can use the formula for the electric field due to a charged line or rod:

E = k * (λ / r)

Where:
E is the electric field
k is the electrostatic constant (8.99 x 10^9 Nm^2/C^2)
λ is the charge per unit length
r is the distance from the axis of the rod

a) For a distance of 3.00 cm (or 0.03 m), we can calculate the electric field as follows:

E = (8.99 x 10^9 Nm^2/C^2) * (30.0 x 10^-9 C/m) / (0.03 m)

Simplifying the calculation, we get:

E = 8.99 x 10^9 Nm^2/C^2 * 1.0 x 10^-6 C/m

E = 8.99 x 10^3 N/C

Therefore, the electric field at a distance of 3.00 cm from the axis of the rod is 8.99 x 10^3 N/C.

b) For a distance of 13.5 cm (or 0.135 m), we can use the same formula:

E = (8.99 x 10^9 Nm^2/C^2) * (30.0 x 10^-9 C/m) / (0.135 m)

Simplifying the calculation, we get:

E = 8.99 x 10^9 Nm^2/C^2 * 2.22 x 10^-7 C/m

E = 2.00 N/C

Therefore, the electric field at a distance of 13.5 cm from the axis of the rod is 2.00 N/C.

c) For a distance of 120 cm (or 1.20 m), we can use the same formula:

E = (8.99 x 10^9 Nm^2/C^2) * (30.0 x 10^-9 C/m) / (1.20 m)

Simplifying the calculation, we get:

E = 8.99 x 10^9 Nm^2/C^2 * 2.50 x 10^-8 C/m

E = 0.225 N/C

Therefore, the electric field at a distance of 120 cm from the axis of the rod is 0.225 N/C.