Question

A long, straight metal rod has a radius of 5.70 cm and a charge per unit length of 28.2 nC/m. Find the electric field at the following distances from the axis of the rod, where distances are measured perpendicular to the rod's axis. (a) 3.10 cm magnitude N/C direction (b) 18.0 cm magnitude N/C direction(c) 180 cm magnitude N/C direction

Answer 1

Answer:

0

2817.43213 N/C

281.74321 N/C

Explanation:

The metal rod is conducting electricity. This means that the charges are being carried on the surface. Inside the rod there is no electric field. So, the electric field intensity is zero at a distance 3.1 cm.

$\epsilon_0$ = Permittivity of free space = $8.85\times 10^{-12}\ F/m$

r = Distance

$\lambda$ = Charge per unit length = 28.2 nC/m

Electric field is given by

$E=\dfrac{\lambda}{2\pi \epsilon_0r}\\\Rightarrow E=\dfrac{28.2\times 10^{-9}}{2\pi \times 8.85\times 10^{-12}\times 0.18}\\\Rightarrow E=2817.43213\ N/C$

The electric field intensity is 2817.43213 N/C

$E=\dfrac{\lambda}{2\pi \epsilon_0r}\\\Rightarrow E=\dfrac{28.2\times 10^{-9}}{2\pi \times 8.85\times 10^{-12}\times 1.8}\\\Rightarrow E=281.74321\ N/C$

The electric field intensity is 281.74321 N/C