A charge of uniform density (0.74 nC/m) is distributed along the x axis from the origin to the point x = 10 cm. What is the electric potential (relative to zero at infinity) at a point, x = 23 cm, on the x axis? Hint: Use Calculus to solve this problem.

 V = - 3.85 V

Explanation:

The electric potential of a continuous charge distribution is

       V = k ∫ dq / r

to find charge differential let's use the concept of linear density

        λ = dq / dx

       dq = λ dx

the distance from a load element to the point of interest

       x₀ = 23 cm = 0.23 m

       r = √ (x-x₀)² = x - x₀

we substitute

        v = k ∫ λ dx / (x-x₀)

we integrate and evaluate between x = 0 and x = l = 0.10 cm

       V = k λ [ln (x-x₀) - ln (-x₀)]

        V = k λ ln ((x-x₀) / x₀)

let's calculate

         V = 9 10⁹  0.74 10⁻⁹ ln ((0.23 - 0.10) / 0.23)

          V = - 3.85 V

spectral lines lyman is one set

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.