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)

weather forecasts are done by collecting data about the current state of the atmosphere mainly the temperature, humidity and wind and using meteorology, to determine the atmosphere that evolves over time. the h and l mean the high and low pressure. the red strip is a warm front. the blue strip is a cold front. the blue and red strip is a stationary front. the purple strip is a occluded front.

explanation:

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