Positive charge q is distributed uniformly along the x-axis from x=0 to x=a. a positive point charge q is located on the positive x-axis at point x-atr, a distance r to the right from the end of q. (a) using integral calculus, calculate the elect field produced by the charge distribution all points x > a. (b) what is the force on the small charge q (c) if/> > a, what is the force on q?

 electric field E = - k Q (1 /r(r-a)), force    F = - k Q qo / r (r-a) and force for r>>a    F ≈ - k Q qo / r²

Explanation:

You are asked to find the electric field of a continuous charge distribution, so we must use the equation

           E = k ∫dp /r²

Where k is the Coulomb constant that is worth 8.99 10⁹ N m² / C², r is the distance between the load distribution and the test charge, in this case everything is on the X axis.

We must find the charge differential (dq), let's use that uniformly distributed and create a linear charge density

          λ = q / x

As it is constant, we can write it based on differentials

         λ = dq / dx

         dq = λ dx

We already have all the terms, let's  integrate enter its limits, lower the distance from the left end of the distribution to the test charge (x = r) and the upper limit that is the distance from the left end of distribution to the test load ( x = r - a) where r> a

         E = k ∫ λ dx / x²

         E = k la (- 1 / x)

Let's get the negative sign from the parentheses

         E = - k λ (1 / x)

         E = - k λ (1 /(r-a)  -1 /r) = - k λ [a / r (r-a)]

Let's change the charge density with the value of the total charge λ = Q / a

         E = - k Q/a  [a / r (r-a)]

         E = - k Q (1 /r(r-a))

b) We calculate the force.  

         F = E qo

         F = - k Q qo / r (r-a)

c) the force for charge porbe very far r >> a. In this case we can take r from the parentheses and neglect (a/r)

         F = - k Qqo / r² (1 -  a/r)

         F ≈ - k Q qo / r²

explanation:

earth's surface is mainly heated by the absorption of infrared radiation from the sun.

evaporation occurs because molecules in liquid water are warmed ( usually by the sun) and vibrate quicker, becoming less dense and rise.

condensation occurs because molecules in water vapor are cooled and therefore vibrate more slowly thus becoming more dense and eventually fall to earth.

lines of equal barometric pressure on a weather map are called: isobars : lines of equal temp on a weather map are called: isotherms.​

friction

explanation:

they us to move forward and backwards