A charge Q is distributed uniformly along the x axis from x1 to x2. What would be the magnitude of the electric field at x0 on the x-axis? Assume that ke = 1 4 π ǫ0 and x0 > x2 > x1 for a Coulomb constant of 8.98755 × 109 N · m2 /C 2

The magnitude of electric field at x0 on the x-axis is  E = k Q   1 / (x₀-x₂) (x₀-x₁).  

The electric field can be calculated by  

dE = k dq / r²

Where,

dE - electric field

k - Coulomb constant of 8.98755 × 109 N · m2 /C 2

dq - Charge

r - distance between two point  

The linear density  

λ = Q / x = dq / dx  

dq = λ dx

Put the values in the equation,  

∫ dE = k ∫ λ dx / x²

Now, integrate  

E = k λ (-1 / x)

Calculate, between the lower limits x = x₀- x₂ and higher x = x₀-x₁  

E = k λ (-1 / x₀-x₁ + 1 / x₀-x₂)  

E = k λ  (x₂ -x₁) / (x₀-x₂) (x₀-x₁)

Replace the density  

E = k (Q / (x₂-x₁)) [(x₂-x₁) / (x₀-x₂) (x₀-x₁)]  

E =  k Q    1 / (x₀-x₂) (x₀-x₁)

Therefore, the magnitude of electric field at x0 on the x-axis is  E = k Q [1 / (x₀-x₂) (x₀-x₁)].

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  E =  k Q    1 / (x₀-x₂) (x₀-x₁)

Explanation:

The electric field is given by

              dE = k dq / r²

In this case as we have a continuous load distribution we can use the concept of linear density

              λ= Q / x = dq / dx

              dq = λ dx

We substitute in the equation

           ∫ dE = k ∫ λ dx / x²

We integrate

           E = k λ (-1 / x)

We evaluate between the lower limits x = x₀- x₂ and higher x = x₀-x₁

           E = k λ (-1 / x₀-x₁ + 1 / x₀-x₂)

           E = k λ  (x₂ -x₁) / (x₀-x₂) (x₀-x₁)

We replace the density

             E = k (Q / (x₂-x₁)) [(x₂-x₁) / (x₀-x₂) (x₀-x₁)]

             E =  k Q    1 / (x₀-x₂) (x₀-x₁)

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force