Calculate the electric field at a distance z=4.00 m above one end of a straight line segment charge

What is the electric field at a distance z=4.00 m above one end of a straight line segment charge?

Given information: Length of the line charge, L=10.2 m, line charge density, λ=1.14 C/m, Electric field, E=?, Distance from one end of the line, z=4 m

Electric Field Calculation

The electric field at a distance z=4.00 m above one end of a straight line segment charge of length L=10.2 m and uniform line charge density λ=1.14 Cm ​−1 can be calculated using the formula: E = λ/2πε₀z (1 - x/√(L² + z²)).

Explanation

In this case, x=0 as we are calculating the electric field at a distance z from one end of the line. Therefore, E = λ/2πε₀z (1 - 0/√(L² + z²)).

By substituting the given values into the formula, we get: E= (1.14 × 10⁻⁶)/(2 × π × 8.85 × 10⁻¹² × 4) (1 - 0/√(10.2² + 4²)) = 4.31 × 10⁻⁶ N/C.

Thus, the electric field at a distance z=4.00 m above one end of a straight line segment charge of length L=10.2 m and uniform line charge density λ=1.14 Cm ​−1 is 4.31 × 10⁻⁶ N/C.