Find Electrical field.

Question

 A straight rod has a charge of +230nC distributed along its 6.3 m length . Estimate E near the middle of the rod at a perpendicular distance of 25mm.

Answer 1

Near the center of the rod, close to the rod, the electric lines are parallel and remain perpendicular to the rod.

Let's take a cylindrical volume around the rod near the center with radius r= 25mm = 0.025 m. Let the height of cylinder be h.

Assuming uniform distribution of charge of the rod, charge distribution λ = 230nC/6.3 m = 230/6.3 nC/m

Charge enclosed the cylinder = λ h

Integral E .dS over the cylinder = E*(2πrh)

ε₀E*(2πrh) = λ h [ by Gauss Law ]

E = λ/2πε₀r = (1/4πε₀) * 2 λ/r = 9*10⁹ *2 *(230*10^-9/6.3 )/0.025 V/m = 2.63*10⁴V/m [ 3 significant digits]